Fixed Effects Tests

Abstract

Show how different FE’s absorb different variation in the data.

```{r}
#| message: false
#| warning: false
#| label: prepare-data

library(tidyverse)
library(fixest)
library(haven)
library(kableExtra)
library(modelsummary)
library(ggplot2)
library(patchwork)
library(DescTools)
library(broom)
library(tibble)
library(purrr)
library(plotly)

# Don't include grid lines in ggplot, only axes
theme_set(theme_minimal())

df <- read_dta("/Users/st2246/Work/Pilot3/data/generated/main/transform/30_merged_panel-hh_id-period.dta") %>%
    mutate(
        treatment = as.factor(treatment),
        treatment_split = as.factor(treatment_split),
        treatment_balanced = as.factor(treatment_balanced),
        enum_id = as.factor(enum_id),
        # Make sure draw is non-empty for control arms too
        draw_realized = ifelse(treatment == 0, "C", draw_realized),
        draw_imputed = ifelse(treatment == 0, "C", draw_imputed),
        draw_imputed_lag1 = ifelse(treatment == 0, "C", draw_imputed_lag1),
        draw_realized_lag1 = ifelse(treatment == 0, "C", draw_realized_lag1),
        pass_bags = if_else(is.na(pass_bags), 0, pass_bags),
        study_income = as.numeric(pass_bags * 12),
        study_income = if_else(treatment == 0, 0, study_income),
        study_income = if_else(pickup_completed == 0, 0, study_income),
        # high = draw == "H"
        hh_size = as.numeric(hh_size),
        hh_id = as.factor(hh_id)
    )

# Define variables to analyze
variables <- c(
    "total_consumption_99",
    "gad2_z",
    "phq2_z",
    "total_income_99"
)


# Create baseline values using filter + join approach
baseline_df <- df %>%
    filter(period == 0) %>%
    select(hh_id, all_of(variables)) %>%
    rename_with(~ paste0(.x, "_bl"), .cols = -hh_id)

df <- df %>%
    left_join(baseline_df, by = "hh_id")
```

```{r}
#| message: false
#| warning: false
#| label: useful-functions
# Function to run regressions for a variable
run_regressions <- function(
    var,
    fe_spec,
    varLabel = variableLabels[var],
    reg_data = df,
    controls = paste0(var, "_bl + hh_size + wealth_index")) {
    formula <- paste0(var, " ~ i(treatment)")
    if (fe_spec != "None") {
        formula <- paste0(var, " ~ i(treatment) | ", fe_spec)
    }

    # By Treatment groups
    model <- feols(as.formula(formula),
        cluster = "community_id",
        data = reg_data
    )
    model
}

model_to_ses <- function(model, name) {
    result <- model %>%
        tidy() %>%
        # Only keep terms with "treatment::"
        filter(str_detect(term, "treatment::")) %>%
        # Keep the min, max and avg of std.error
        summarise(
            min_se = min(std.error),
            max_se = max(std.error),
            avg_se = mean(std.error)
        ) %>%
        mutate(
            fe_spec = name
        )
    result
}

# Make basic tables using modelsummary and kableExtra to show results
variableLabels <- c(
    "total_consumption_99" = "Total Consumption",
    "gad2_z" = "GAD-2 Z-Score",
    "phq2_z" = "PHQ-2 Z-Score",
    "total_income_99" = "Total Income"
)

makeTable <- function(models) {
    table <- modelsummary(models,
        escape = FALSE,
        rename = variableLabels,
        output = "kableExtra",
        estimate = "{estimate}{stars}",
        statistic = "{std.error} ({conf.low}, {conf.high})",
        coef_omit = NULL,
        coef_omit_sources = FALSE,
        stars = c(`***` = 0.01, `**` = 0.05, `*` = 0.1),
        gof_map = tribble(
            ~raw, ~clean, ~fmt,
            "nobs", "Observations", 0,
            "FE", "Community FE", 1,
        )
    ) %>%
        kable_classic(full_width = F, html_font = "Cambria", fixed_thead = T)
    table
}

fe_specs <- c(
    "District Fixed Effects" = "district_id",
    "Community Fixed Effects" = "community_id",
    "Wave Fixed Effects" = "wave",
    "Cohort Fixed Effects" = "cohort",
    "Period Fixed Effects" = "period",
    "Enumerator Fixed Effects" = "enum_id",
    "Day of Survey Fixed Effects" = "day_of_week",
    "Survey on Time" = "on_time"
)
```

1 SE Comparison Across Variables

To help us pick which variables to use as a fixed effects, I’ve the made the following graphs and tables.

The table below shows the regression results for PHQ-2 Z-Score when using a bunch of different potential fixed effects.

```{r}
#| message: false
#| warning: false
#| label: run-estimates

# For the var phq2_z, run regressions for all FE specs and make tables
results <- map(c("None" = "None", fe_specs), ~ {
    run_regressions("phq2_z", .x)
})

makeTable(results)
```

	None	District Fixed Effects	Community Fixed Effects	Wave Fixed Effects	Cohort Fixed Effects	Period Fixed Effects	Enumerator Fixed Effects	Day of Survey Fixed Effects	Survey on Time
(Intercept)	−0.139***
	0.028 (−0.195, −0.084)
treatment = 1	−0.065*	−0.066*	−0.065*	−0.065*	−0.066*	−0.062*	−0.051	−0.064*	−0.066*
	0.035 (−0.134, 0.004)	0.035 (−0.135, 0.003)	0.036 (−0.136, 0.006)	0.035 (−0.134, 0.004)	0.034 (−0.134, 0.003)	0.035 (−0.131, 0.007)	0.033 (−0.116, 0.014)	0.035 (−0.133, 0.005)	0.035 (−0.134, 0.003)
treatment = 2	−0.022	−0.024	−0.033	−0.022	−0.019	−0.020	−0.015	−0.020	−0.022
	0.038 (−0.098, 0.054)	0.038 (−0.100, 0.052)	0.039 (−0.110, 0.043)	0.038 (−0.098, 0.054)	0.040 (−0.098, 0.059)	0.038 (−0.096, 0.056)	0.037 (−0.088, 0.059)	0.039 (−0.096, 0.056)	0.038 (−0.097, 0.054)
treatment = 3	−0.072**	−0.074**	−0.077**	−0.072**	−0.071**	−0.070**	−0.062**	−0.070**	−0.072**
	0.030 (−0.132, −0.012)	0.030 (−0.134, −0.014)	0.031 (−0.138, −0.016)	0.030 (−0.132, −0.012)	0.031 (−0.132, −0.010)	0.030 (−0.130, −0.010)	0.029 (−0.119, −0.004)	0.030 (−0.130, −0.010)	0.030 (−0.132, −0.012)
Observations	14803	14803	14803	14803	14803	14803	14803	14803	14803

```{r}
#| message: false
#| warning: false
make_se_graph <- function(var, fes = c(fe_specs, "None")) {
    visual_results <- map_df(fes, ~ {
        run_regressions(var, .x) %>%
            model_to_ses(.x)
    })

    avg_treatment_coef <- run_regressions(var, "None") %>%
        tidy() %>%
        filter(str_detect(term, "treatment::")) %>%
        summarise(
            avg_coef = abs(mean(estimate))
        ) %>%
        pull(avg_coef)

    visual_results <- visual_results %>%
        mutate(
            fe_spec = fct_reorder(fe_spec, avg_se, .desc = TRUE),
            avg_se_pct_coeff = (avg_se / avg_treatment_coef) * 100
        )

    varName <- variableLabels[[var]]

    plot <- ggplot(visual_results, aes(y = fe_spec)) +
        geom_point(aes(x = avg_se)) +
        geom_errorbar(aes(xmin = min_se, xmax = max_se), width = 0.2) +
        geom_vline(xintercept = avg_treatment_coef, color = "red") +
        labs(
            title = varName,
            x = "SE (min, avg, max)",
            y = NULL
        )

    plot2 <- ggplot(visual_results, aes(y = fe_spec)) +
        geom_point(aes(x = avg_se_pct_coeff)) +
        # Color the point corresponding fe_spec == None as red
        geom_point(data = filter(visual_results, fe_spec == "None"), aes(x = avg_se_pct_coeff), color = "red") +
        labs(
            title = varName,
            x = "SE as % of Coefficient",
            y = NULL
        )
    # Rotate y-axis labels for readability
    plot2 <- plot2 + theme(axis.text.y = element_text(angle = 45, hjust = 1))

    plot2
}
```

Note that the differences are not large, both when comparing between different fixed effects as well as when comparing to having no fixed effects at all.

Below, I show how the SE’s change when using different fixed effects for 4 outcomes:

• Total Consumption
• GAD-2 Z-Score
• PHQ-2 Z-Score
• Total Income

I use the average SE across treatment arms for visualization. I also divide the SE by the average treatment effect coefficient to create a reference point for understanding the magnitude of the SE.

Note that the SEs individual treatment arms are not indentical (in particular, Risky is a bit smaller due to the larger sample size) but they follow similar patterns when changing as seen by the table above.

```{r}
#| fig.width: 12
#| fig.height: 8
#| message: false
#| warning: false
# Used shared y-axis for easier comparison
# Have common x-axis labels
# Add custom x-axis caption
make_se_graph("total_consumption_99") + make_se_graph("gad2_z") + make_se_graph("phq2_z") + make_se_graph("total_income_99") + plot_layout(ncol = 4, axis_titles = "collect")
```

Enumerator Fixed Effects seems to reduce SE’s by noteable amount; the other fixed effects have much less meaninful impact on SE’s (or sometimes increase it). District FEs seem to be helpful for income but not for the other variables.

2 Powerset of Fixed Effects

I also take a look at every combination of the above fixed effects across our 4 different outcomes. The results for the 4 different outcomes are shown in the tabs below.

```{r}
#| label: fe-powerset

fe_power_set_raw <- unlist(lapply(0:length(fe_specs), function(n) {
    combn(fe_specs, n, FUN = list)
}), recursive = FALSE)

fe_power_set <- fe_power_set_raw %>%
    set_names(
        nm = lapply(fe_power_set_raw, function(x) {
            if (length(x) == 0) {
                "No Fixed Effects"
            } else {
                paste(names(x), collapse = " + ")
            }
        })
    )

fe_power_set <- fe_power_set %>%
    map(~ paste(.x, collapse = " + "))

# Replace empty string with "None"
fe_power_set <- fe_power_set %>%
    imap(~ if (.y == "No Fixed Effects") "None" else .x)

power_set_se_df <- function(var) {
    coef <- run_regressions(var, "None") %>%
        tidy() %>%
        filter(str_detect(term, "treatment::")) %>%
        summarise(
            avg_coef = abs(mean(estimate))
        ) %>%
        pull(avg_coef)

    df <- map_df(fe_power_set, ~ {
        run_regressions(var, .x) %>%
            model_to_ses(.x)
    }) %>%
        arrange(avg_se) %>%
        mutate(
            fe_spec = fct_reorder(fe_spec, avg_se, .desc = FALSE),
            avg_se_pct_coeff = (avg_se / coef) * 100,
            none_se = avg_se[fe_spec == "None"],
            avg_se_pct_none = (avg_se / none_se) * 100
        ) %>%
        select(-none_se)
}
```

```{r}
#| warning: false
#| message: false
#| cache: true
#| label: fe-powerset-dfs(SLOW)
phq2_power_set_se <- power_set_se_df("phq2_z")
gad2_power_set_se <- power_set_se_df("gad2_z")
consumption_power_set_se <- power_set_se_df("total_consumption_99")
income_power_set_se <- power_set_se_df("total_income_99")
```

```{r}
#| label: fe-powerset-table-maker

nice_table <- function(df) {
    df %>%
        arrange(avg_se) %>%
        select(fe_spec, avg_se, avg_se_pct_coeff, avg_se_pct_none) %>%
        # Name the columns to be human readable
        rename(
            "FE Specification" = fe_spec,
            "Average SE" = avg_se,
            "As % of Coef." = avg_se_pct_coeff,
            "As % of No FE SE" = avg_se_pct_none
        ) %>%
        kableExtra::kable() %>%
        kableExtra::scroll_box(height = "300px")
        # Limit to 20 rows before scrolling
        

        
}
```

PHQ-2

```{r}
#| warning: false
#| message: false
#| label: tbl-phq2-ses
#| classes: plain

# Display as kable table that is scrollable
# Show the columns in this order
# fe_spec, avg_se, ave_se_pct_coeff, avg_se_pct_none
# drop the other columns

phq2_power_set_se %>%
    nice_table()
```

FE Specification	Average SE	As % of Coef.	As % of No FE SE
district_id + wave + enum_id + day_of_week + on_time	0.0328398	62.01209	95.26186
district_id + wave + enum_id	0.0328496	62.03049	95.29012
district_id + wave + enum_id + on_time	0.0328514	62.03398	95.29549
district_id + wave + enum_id + day_of_week	0.0328524	62.03577	95.29824
district_id + enum_id + day_of_week + on_time	0.0328535	62.03785	95.30142
district_id + enum_id	0.0328648	62.05920	95.33422
district_id + enum_id + day_of_week	0.0328658	62.06113	95.33718
district_id + enum_id + on_time	0.0328662	62.06193	95.33842
wave + enum_id + day_of_week + on_time	0.0329309	62.18402	95.52597
wave + enum_id	0.0329380	62.19747	95.54663
wave + enum_id + on_time	0.0329405	62.20224	95.55395
wave + enum_id + day_of_week	0.0329431	62.20711	95.56144
enum_id + day_of_week + on_time	0.0329464	62.21331	95.57097
district_id + wave + period + enum_id + day_of_week + on_time	0.0329523	62.22444	95.58806
enum_id	0.0329545	62.22865	95.59452
district_id + wave + period + enum_id + day_of_week	0.0329552	62.22995	95.59653
enum_id + on_time	0.0329563	62.23193	95.59958
enum_id + day_of_week	0.0329587	62.23655	95.60667
district_id + period + enum_id + day_of_week + on_time	0.0329623	62.24338	95.61716
district_id + period + enum_id + day_of_week	0.0329651	62.24855	95.62510
district_id + wave + period + enum_id + on_time	0.0329887	62.29317	95.69365
district_id + period + enum_id + on_time	0.0329999	62.31427	95.72606
district_id + wave + period + enum_id	0.0330002	62.31496	95.72712
district_id + period + enum_id	0.0330120	62.33716	95.76122
wave + period + enum_id + day_of_week + on_time	0.0330436	62.39683	95.85289
wave + period + enum_id + day_of_week	0.0330467	62.40278	95.86203
period + enum_id + day_of_week + on_time	0.0330552	62.41883	95.88668
period + enum_id + day_of_week	0.0330584	62.42487	95.89596
wave + period + enum_id + on_time	0.0330768	62.45963	95.94936
wave + period + enum_id	0.0330879	62.48060	95.98157
period + enum_id + on_time	0.0330882	62.48104	95.98225
period + enum_id	0.0331001	62.50350	96.01675
district_id + wave + cohort + enum_id + day_of_week + on_time	0.0331013	62.50584	96.02035
district_id + wave + cohort + enum_id + day_of_week	0.0331120	62.52607	96.05143
district_id + wave + cohort + enum_id + on_time	0.0331206	62.54225	96.07628
district_id + wave + cohort + enum_id	0.0331214	62.54374	96.07857
district_id + cohort + enum_id + day_of_week + on_time	0.0331236	62.54793	96.08501
district_id + cohort + enum_id + day_of_week	0.0331341	62.56775	96.11544
district_id + cohort + enum_id + on_time	0.0331428	62.58410	96.14056
district_id + cohort + enum_id	0.0331439	62.58634	96.14400
district_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0332058	62.70319	96.32352
district_id + wave + cohort + period + enum_id + day_of_week	0.0332077	62.70669	96.32889
wave + cohort + enum_id + day_of_week + on_time	0.0332084	62.70797	96.33085
wave + cohort + enum_id + day_of_week	0.0332185	62.72704	96.36014
community_id + enum_id + day_of_week + on_time	0.0332197	62.72939	96.36376
community_id + wave + enum_id + day_of_week + on_time	0.0332208	62.73152	96.36702
district_id + cohort + period + enum_id + day_of_week + on_time	0.0332218	62.73335	96.36984
district_id + community_id + enum_id + day_of_week + on_time	0.0332231	62.73577	96.37356
district_id + cohort + period + enum_id + day_of_week	0.0332235	62.73653	96.37473
district_id + community_id + wave + enum_id + day_of_week + on_time	0.0332242	62.73790	96.37683
wave + cohort + enum_id + on_time	0.0332279	62.74483	96.38748
wave + cohort + enum_id	0.0332280	62.74510	96.38790
cohort + enum_id + day_of_week + on_time	0.0332323	62.75322	96.40037
community_id + enum_id + on_time	0.0332391	62.76606	96.42009
community_id + wave + enum_id + on_time	0.0332403	62.76821	96.42339
cohort + enum_id + day_of_week	0.0332425	62.77249	96.42996
district_id + community_id + enum_id + on_time	0.0332425	62.77249	96.42997
district_id + wave + cohort + period + enum_id + on_time	0.0332428	62.77295	96.43068
district_id + community_id + wave + enum_id + on_time	0.0332437	62.77463	96.43326
community_id + enum_id	0.0332468	62.78054	96.44234
community_id + enum_id + day_of_week	0.0332479	62.78268	96.44562
community_id + wave + enum_id	0.0332479	62.78269	96.44564
community_id + wave + enum_id + day_of_week	0.0332490	62.78481	96.44890
district_id + community_id + enum_id	0.0332502	62.78698	96.45222
cohort + enum_id + on_time	0.0332506	62.78770	96.45333
district_id + community_id + enum_id + day_of_week	0.0332513	62.78908	96.45545
district_id + community_id + wave + enum_id	0.0332513	62.78912	96.45551
cohort + enum_id	0.0332515	62.78938	96.45592
district_id + community_id + wave + enum_id + day_of_week	0.0332524	62.79120	96.45871
district_id + wave + cohort + period + enum_id	0.0332561	62.79808	96.46927
district_id + cohort + period + enum_id + on_time	0.0332601	62.80569	96.48097
district_id + cohort + period + enum_id	0.0332741	62.83210	96.52154
wave + cohort + period + enum_id + day_of_week + on_time	0.0333178	62.91458	96.64824
wave + cohort + period + enum_id + day_of_week	0.0333198	62.91836	96.65405
cohort + period + enum_id + day_of_week + on_time	0.0333351	62.94721	96.69838
cohort + period + enum_id + day_of_week	0.0333371	62.95113	96.70439
community_id + period + enum_id + day_of_week + on_time	0.0333401	62.95666	96.71288
community_id + wave + period + enum_id + day_of_week + on_time	0.0333412	62.95880	96.71617
district_id + community_id + period + enum_id + day_of_week + on_time	0.0333435	62.96308	96.72275
district_id + community_id + wave + period + enum_id + day_of_week + on_time	0.0333446	62.96523	96.72606
community_id + period + enum_id + day_of_week	0.0333513	62.97782	96.74539
community_id + wave + period + enum_id + day_of_week	0.0333524	62.97997	96.74870
wave + cohort + period + enum_id + on_time	0.0333537	62.98242	96.75245
district_id + community_id + period + enum_id + day_of_week	0.0333547	62.98424	96.75526
district_id + community_id + wave + period + enum_id + day_of_week	0.0333558	62.98640	96.75857
wave + cohort + period + enum_id	0.0333666	63.00670	96.78976
cohort + period + enum_id + on_time	0.0333707	63.01452	96.80178
cohort + period + enum_id	0.0333844	63.04041	96.84154
community_id + period + enum_id + on_time	0.0333887	63.04854	96.85402
community_id + wave + period + enum_id + on_time	0.0333899	63.05071	96.85736
district_id + community_id + period + enum_id + on_time	0.0333921	63.05499	96.86394
district_id + community_id + wave + period + enum_id + on_time	0.0333933	63.05712	96.86722
community_id + period + enum_id	0.0334111	63.09082	96.91897
community_id + wave + period + enum_id	0.0334122	63.09296	96.92227
district_id + community_id + period + enum_id	0.0334145	63.09725	96.92886
district_id + community_id + wave + period + enum_id	0.0334156	63.09941	96.93218
community_id + cohort + enum_id + day_of_week + on_time	0.0335918	63.43198	97.44306
community_id + wave + cohort + enum_id + day_of_week + on_time	0.0335929	63.43414	97.44639
district_id + community_id + cohort + enum_id + day_of_week + on_time	0.0335952	63.43845	97.45300
district_id + community_id + wave + cohort + enum_id + day_of_week + on_time	0.0335963	63.44062	97.45634
community_id + cohort + enum_id + on_time	0.0336158	63.47741	97.51286
community_id + cohort + enum_id + day_of_week	0.0336166	63.47896	97.51523
community_id + wave + cohort + enum_id + on_time	0.0336170	63.47958	97.51618
community_id + wave + cohort + enum_id + day_of_week	0.0336178	63.48109	97.51850
district_id + community_id + cohort + enum_id + on_time	0.0336193	63.48391	97.52284
district_id + community_id + cohort + enum_id + day_of_week	0.0336201	63.48541	97.52515
district_id + community_id + wave + cohort + enum_id + on_time	0.0336204	63.48606	97.52613
district_id + community_id + wave + cohort + enum_id + day_of_week	0.0336212	63.48758	97.52847
community_id + cohort + enum_id	0.0336237	63.49223	97.53561
community_id + wave + cohort + enum_id	0.0336248	63.49440	97.53895
district_id + community_id + cohort + enum_id	0.0336271	63.49873	97.54560
district_id + community_id + wave + cohort + enum_id	0.0336283	63.50087	97.54889
community_id + cohort + period + enum_id + day_of_week + on_time	0.0336948	63.62659	97.74202
community_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0336960	63.62876	97.74535
district_id + community_id + cohort + period + enum_id + day_of_week + on_time	0.0336983	63.63310	97.75202
district_id + community_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0336994	63.63526	97.75534
community_id + cohort + period + enum_id + day_of_week	0.0337035	63.64305	97.76731
community_id + wave + cohort + period + enum_id + day_of_week	0.0337047	63.64522	97.77064
district_id + community_id + cohort + period + enum_id + day_of_week	0.0337070	63.64953	97.77726
district_id + community_id + wave + cohort + period + enum_id + day_of_week	0.0337081	63.65171	97.78061
community_id + cohort + period + enum_id + on_time	0.0337355	63.70334	97.85992
community_id + wave + cohort + period + enum_id + on_time	0.0337366	63.70550	97.86324
district_id + community_id + cohort + period + enum_id + on_time	0.0337389	63.70983	97.86989
district_id + community_id + wave + cohort + period + enum_id + on_time	0.0337401	63.71201	97.87323
community_id + cohort + period + enum_id	0.0337574	63.74478	97.92359
community_id + wave + cohort + period + enum_id	0.0337586	63.74695	97.92691
district_id + community_id + cohort + period + enum_id	0.0337609	63.75128	97.93356
district_id + community_id + wave + cohort + period + enum_id	0.0337620	63.75347	97.93693
district_id + wave + period + on_time	0.0343604	64.88333	99.67259
district_id + wave + period + day_of_week	0.0343669	64.89566	99.69154
district_id + wave + period + day_of_week + on_time	0.0343723	64.90595	99.70735
district_id + wave + period	0.0343771	64.91498	99.72123
district_id + period + on_time	0.0343879	64.93526	99.75238
wave + period + on_time	0.0343945	64.94777	99.77159
wave + period + day_of_week	0.0343965	64.95155	99.77740
district_id + wave + on_time	0.0343968	64.95212	99.77827
wave + period + day_of_week + on_time	0.0344014	64.96075	99.79154
district_id + period + day_of_week	0.0344016	64.96119	99.79221
district_id + period	0.0344041	64.96598	99.79957
district_id + period + day_of_week + on_time	0.0344068	64.97100	99.80727
period + on_time	0.0344076	64.97248	99.80956
wave + period	0.0344105	64.97797	99.81799
period + day_of_week	0.0344186	64.99326	99.84147
district_id + on_time	0.0344220	64.99972	99.85139
period + day_of_week + on_time	0.0344226	65.00082	99.85309
period	0.0344234	65.00245	99.85558
district_id + wave	0.0344263	65.00777	99.86376
wave + on_time	0.0344351	65.02447	99.88942
on_time	0.0344457	65.04453	99.92024
district_id	0.0344513	65.05514	99.93654
wave	0.0344622	65.07559	99.96795
None	0.0344732	65.09645	100.00000
district_id + wave + day_of_week + on_time	0.0345004	65.14773	100.07876
district_id + wave + day_of_week	0.0345110	65.16772	100.10947
wave + day_of_week + on_time	0.0345258	65.19572	100.15249
district_id + day_of_week + on_time	0.0345317	65.20692	100.16969
wave + day_of_week	0.0345350	65.21311	100.17920
day_of_week + on_time	0.0345420	65.22623	100.19936
district_id + day_of_week	0.0345420	65.22637	100.19958
day_of_week	0.0345519	65.24497	100.22815
district_id + wave + cohort + period + day_of_week	0.0347565	65.63127	100.82158
district_id + wave + cohort + period + on_time	0.0347591	65.63634	100.82937
district_id + wave + cohort + period + day_of_week + on_time	0.0347622	65.64209	100.83819
district_id + wave + cohort + period	0.0347758	65.66772	100.87757
district_id + cohort + period + on_time	0.0347864	65.68781	100.90843
district_id + cohort + period + day_of_week	0.0347902	65.69495	100.91939
district_id + wave + cohort + on_time	0.0347950	65.70398	100.93327
district_id + cohort + period + day_of_week + on_time	0.0347958	65.70552	100.93563
district_id + cohort + period	0.0348028	65.71873	100.95592
district_id + cohort + on_time	0.0348199	65.75111	101.00566
district_id + wave + cohort	0.0348243	65.75939	101.01839
district_id + cohort	0.0348494	65.80677	101.09118
wave + cohort + period + day_of_week	0.0348585	65.82398	101.11761
wave + cohort + period + day_of_week + on_time	0.0348649	65.83607	101.13618
wave + cohort + period + on_time	0.0348704	65.84641	101.15207
district_id + wave + cohort + day_of_week + on_time	0.0348769	65.85870	101.17095
cohort + period + day_of_week	0.0348841	65.87238	101.19197
wave + cohort + period	0.0348853	65.87460	101.19537
cohort + period + on_time	0.0348876	65.87884	101.20189
district_id + wave + cohort + day_of_week	0.0348885	65.88061	101.20461
cohort + period + day_of_week + on_time	0.0348898	65.88315	101.20851
cohort + period	0.0349027	65.90735	101.24569
district_id + cohort + day_of_week + on_time	0.0349093	65.91997	101.26508
wave + cohort + on_time	0.0349102	65.92156	101.26751
district_id + cohort + day_of_week	0.0349205	65.94106	101.29747
cohort + on_time	0.0349248	65.94916	101.30991
community_id + period + day_of_week + on_time	0.0349355	65.96938	101.34098
wave + cohort	0.0349363	65.97091	101.34332
community_id + wave + period + day_of_week + on_time	0.0349367	65.97162	101.34441
district_id + community_id + period + day_of_week + on_time	0.0349390	65.97607	101.35125
district_id + community_id + wave + period + day_of_week + on_time	0.0349402	65.97830	101.35468
community_id + period + day_of_week	0.0349424	65.98238	101.36095
community_id + period + on_time	0.0349427	65.98297	101.36185
community_id + wave + period + day_of_week	0.0349436	65.98462	101.36438
community_id + wave + period + on_time	0.0349439	65.98520	101.36528
district_id + community_id + period + day_of_week	0.0349459	65.98908	101.37123
district_id + community_id + period + on_time	0.0349462	65.98966	101.37213
district_id + community_id + wave + period + day_of_week	0.0349471	65.99131	101.37466
district_id + community_id + wave + period + on_time	0.0349474	65.99189	101.37556
cohort	0.0349517	65.99999	101.38800
community_id + on_time	0.0349703	66.03514	101.44199
community_id + wave + on_time	0.0349715	66.03737	101.44542
district_id + community_id + on_time	0.0349739	66.04184	101.45228
district_id + community_id + wave + on_time	0.0349751	66.04407	101.45571
wave + cohort + day_of_week + on_time	0.0349760	66.04576	101.45830
wave + cohort + day_of_week	0.0349848	66.06243	101.48391
community_id + period	0.0349878	66.06806	101.49257
community_id + wave + period	0.0349889	66.07029	101.49600
district_id + community_id + period	0.0349913	66.07476	101.50286
district_id + community_id + wave + period	0.0349925	66.07700	101.50629
cohort + day_of_week + on_time	0.0349992	66.08959	101.52563
cohort + day_of_week	0.0350085	66.10723	101.55273
community_id	0.0350298	66.14735	101.61437
community_id + wave	0.0350309	66.14959	101.61780
district_id + community_id	0.0350333	66.15406	101.62467
district_id + community_id + wave	0.0350345	66.15629	101.62810
community_id + day_of_week + on_time	0.0350494	66.18452	101.67147
community_id + wave + day_of_week + on_time	0.0350506	66.18676	101.67491
district_id + community_id + day_of_week + on_time	0.0350530	66.19124	101.68179
district_id + community_id + wave + day_of_week + on_time	0.0350542	66.19348	101.68523
community_id + day_of_week	0.0350996	66.27930	101.81706
community_id + wave + day_of_week	0.0351008	66.28154	101.82050
district_id + community_id + day_of_week	0.0351032	66.28602	101.82739
district_id + community_id + wave + day_of_week	0.0351044	66.28826	101.83083
community_id + cohort + period + day_of_week + on_time	0.0354007	66.84774	102.69029
community_id + wave + cohort + period + day_of_week + on_time	0.0354019	66.85000	102.69376
community_id + cohort + period + on_time	0.0354019	66.85002	102.69379
community_id + wave + cohort + period + on_time	0.0354031	66.85228	102.69727
community_id + cohort + period + day_of_week	0.0354035	66.85311	102.69855
district_id + community_id + cohort + period + day_of_week + on_time	0.0354042	66.85452	102.70070
community_id + wave + cohort + period + day_of_week	0.0354047	66.85537	102.70201
district_id + community_id + wave + cohort + period + day_of_week + on_time	0.0354054	66.85678	102.70418
district_id + community_id + cohort + period + on_time	0.0354055	66.85680	102.70421
district_id + community_id + wave + cohort + period + on_time	0.0354067	66.85906	102.70768
district_id + community_id + cohort + period + day_of_week	0.0354071	66.85988	102.70895
district_id + community_id + wave + cohort + period + day_of_week	0.0354083	66.86215	102.71243
community_id + cohort + on_time	0.0354175	66.87956	102.73917
community_id + wave + cohort + on_time	0.0354187	66.88182	102.74264
district_id + community_id + cohort + on_time	0.0354211	66.88634	102.74959
district_id + community_id + wave + cohort + on_time	0.0354223	66.88860	102.75306
community_id + cohort + period	0.0354440	66.92962	102.81608
community_id + wave + cohort + period	0.0354452	66.93189	102.81956
district_id + community_id + cohort + period	0.0354476	66.93641	102.82651
district_id + community_id + wave + cohort + period	0.0354488	66.93867	102.82998
community_id + cohort	0.0354736	66.98550	102.90191
community_id + wave + cohort	0.0354748	66.98776	102.90539
district_id + community_id + cohort	0.0354772	66.99229	102.91235
district_id + community_id + wave + cohort	0.0354784	66.99455	102.91582
community_id + cohort + day_of_week + on_time	0.0354863	67.00950	102.93879
community_id + wave + cohort + day_of_week + on_time	0.0354875	67.01177	102.94228
district_id + community_id + cohort + day_of_week + on_time	0.0354899	67.01630	102.94923
district_id + community_id + wave + cohort + day_of_week + on_time	0.0354911	67.01857	102.95272
community_id + cohort + day_of_week	0.0355247	67.08198	103.05012
community_id + wave + cohort + day_of_week	0.0355259	67.08426	103.05362
district_id + community_id + cohort + day_of_week	0.0355283	67.08876	103.06055
district_id + community_id + wave + cohort + day_of_week	0.0355295	67.09104	103.06404

GAD-2

```{r}
#| warning: false
#| message: false
#| label: tbl-gad2-ses
#| classes: plain

gad2_power_set_se %>%
    nice_table()
```

FE Specification	Average SE	As % of Coef.	As % of No FE SE
community_id + period + enum_id + day_of_week + on_time	0.0331696	64.55529	91.70982
community_id + wave + period + enum_id + day_of_week + on_time	0.0331708	64.55749	91.71295
district_id + community_id + period + enum_id + day_of_week + on_time	0.0331730	64.56190	91.71920
district_id + community_id + wave + period + enum_id + day_of_week + on_time	0.0331742	64.56409	91.72232
community_id + period + enum_id + day_of_week	0.0331880	64.59111	91.76071
community_id + wave + period + enum_id + day_of_week	0.0331892	64.59331	91.76384
district_id + community_id + period + enum_id + day_of_week	0.0331914	64.59771	91.77008
district_id + community_id + wave + period + enum_id + day_of_week	0.0331926	64.59990	91.77320
district_id + wave + period + enum_id + day_of_week + on_time	0.0332003	64.61500	91.79465
district_id + wave + enum_id	0.0332023	64.61896	91.80027
district_id + wave + period + enum_id + day_of_week	0.0332057	64.62551	91.80958
district_id + wave + enum_id + day_of_week + on_time	0.0332092	64.63232	91.81925
district_id + period + enum_id + day_of_week + on_time	0.0332152	64.64406	91.83593
district_id + period + enum_id + day_of_week	0.0332198	64.65300	91.84862
district_id + enum_id	0.0332254	64.66390	91.86411
wave + period + enum_id + day_of_week + on_time	0.0332307	64.67419	91.87873
wave + period + enum_id + day_of_week	0.0332341	64.68071	91.88800
district_id + enum_id + day_of_week + on_time	0.0332384	64.68906	91.89986
community_id + enum_id	0.0332390	64.69022	91.90151
community_id + enum_id + day_of_week + on_time	0.0332399	64.69205	91.90410
community_id + wave + enum_id	0.0332401	64.69250	91.90474
community_id + wave + enum_id + day_of_week + on_time	0.0332410	64.69427	91.90726
period + enum_id + day_of_week + on_time	0.0332411	64.69437	91.90740
wave + enum_id	0.0332415	64.69511	91.90845
district_id + wave + enum_id + day_of_week	0.0332417	64.69560	91.90914
district_id + community_id + enum_id	0.0332424	64.69688	91.91097
district_id + community_id + enum_id + day_of_week + on_time	0.0332433	64.69860	91.91341
district_id + community_id + wave + enum_id	0.0332435	64.69908	91.91409
period + enum_id + day_of_week	0.0332440	64.69995	91.91533
district_id + community_id + wave + enum_id + day_of_week + on_time	0.0332444	64.70080	91.91654
district_id + wave + enum_id + on_time	0.0332457	64.70326	91.92004
community_id + period + enum_id	0.0332541	64.71965	91.94331
community_id + wave + period + enum_id	0.0332552	64.72185	91.94645
district_id + community_id + period + enum_id	0.0332575	64.72626	91.95270
district_id + community_id + wave + period + enum_id	0.0332586	64.72846	91.95583
wave + enum_id + day_of_week + on_time	0.0332590	64.72916	91.95683
enum_id	0.0332625	64.73607	91.96664
district_id + wave + period + enum_id	0.0332640	64.73893	91.97070
district_id + enum_id + on_time	0.0332685	64.74765	91.98310
community_id + period + enum_id + on_time	0.0332690	64.74868	91.98455
district_id + enum_id + day_of_week	0.0332695	64.74970	91.98601
community_id + wave + period + enum_id + on_time	0.0332701	64.75088	91.98768
district_id + community_id + period + enum_id + on_time	0.0332724	64.75529	91.99394
district_id + community_id + wave + period + enum_id + on_time	0.0332735	64.75750	91.99708
district_id + period + enum_id	0.0332781	64.76630	92.00959
district_id + wave + period + enum_id + on_time	0.0332794	64.76893	92.01332
community_id + enum_id + on_time	0.0332862	64.78208	92.03201
community_id + wave + enum_id + on_time	0.0332873	64.78428	92.03513
enum_id + day_of_week + on_time	0.0332873	64.78434	92.03522
wave + enum_id + day_of_week	0.0332887	64.78699	92.03898
district_id + community_id + enum_id + on_time	0.0332896	64.78868	92.04138
district_id + community_id + wave + enum_id + on_time	0.0332907	64.79089	92.04452
wave + enum_id + on_time	0.0332911	64.79174	92.04574
wave + period + enum_id	0.0332918	64.79303	92.04757
district_id + period + enum_id + on_time	0.0332926	64.79454	92.04970
community_id + enum_id + day_of_week	0.0332989	64.80694	92.06732
community_id + wave + enum_id + day_of_week	0.0333001	64.80914	92.07046
period + enum_id	0.0333008	64.81048	92.07235
district_id + community_id + enum_id + day_of_week	0.0333023	64.81354	92.07670
district_id + community_id + wave + enum_id + day_of_week	0.0333035	64.81576	92.07986
wave + period + enum_id + on_time	0.0333093	64.82716	92.09605
enum_id + on_time	0.0333118	64.83195	92.10285
enum_id + day_of_week	0.0333162	64.84047	92.11496
period + enum_id + on_time	0.0333172	64.84255	92.11792
community_id + cohort + period + enum_id + day_of_week + on_time	0.0333806	64.96594	92.29321
community_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0333818	64.96816	92.29635
district_id + community_id + cohort + period + enum_id + day_of_week + on_time	0.0333840	64.97257	92.30262
district_id + community_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0333852	64.97477	92.30574
community_id + cohort + period + enum_id + day_of_week	0.0333963	64.99649	92.33661
community_id + wave + cohort + period + enum_id + day_of_week	0.0333975	64.99872	92.33977
district_id + community_id + cohort + period + enum_id + day_of_week	0.0333997	65.00311	92.34601
district_id + community_id + wave + cohort + period + enum_id + day_of_week	0.0334009	65.00533	92.34916
community_id + cohort + enum_id + day_of_week + on_time	0.0334353	65.07232	92.44433
community_id + wave + cohort + enum_id + day_of_week + on_time	0.0334364	65.07453	92.44748
district_id + community_id + cohort + enum_id + day_of_week + on_time	0.0334387	65.07888	92.45366
district_id + community_id + wave + cohort + enum_id + day_of_week + on_time	0.0334398	65.08110	92.45681
community_id + cohort + enum_id	0.0334536	65.10793	92.49492
community_id + wave + cohort + enum_id	0.0334547	65.11015	92.49808
district_id + community_id + cohort + enum_id	0.0334570	65.11455	92.50433
district_id + community_id + wave + cohort + enum_id	0.0334581	65.11674	92.50743
district_id + wave + cohort + period + enum_id + day_of_week + on_time	0.0334599	65.12017	92.51232
district_id + wave + cohort + enum_id + day_of_week + on_time	0.0334615	65.12341	92.51692
community_id + cohort + period + enum_id	0.0334631	65.12644	92.52122
community_id + wave + cohort + period + enum_id	0.0334642	65.12866	92.52437
district_id + wave + cohort + period + enum_id + day_of_week	0.0334660	65.13217	92.52936
district_id + community_id + cohort + period + enum_id	0.0334665	65.13307	92.53064
district_id + community_id + wave + cohort + period + enum_id	0.0334676	65.13528	92.53378
community_id + cohort + period + enum_id + on_time	0.0334741	65.14779	92.55155
community_id + wave + cohort + period + enum_id + on_time	0.0334752	65.15001	92.55470
district_id + community_id + cohort + period + enum_id + on_time	0.0334775	65.15446	92.56102
district_id + community_id + wave + cohort + period + enum_id + on_time	0.0334786	65.15664	92.56412
district_id + cohort + period + enum_id + day_of_week + on_time	0.0334846	65.16827	92.58065
community_id + cohort + enum_id + day_of_week	0.0334858	65.17064	92.58401
community_id + wave + cohort + enum_id + day_of_week	0.0334870	65.17286	92.58717
district_id + wave + cohort + enum_id	0.0334870	65.17300	92.58736
district_id + community_id + cohort + enum_id + day_of_week	0.0334892	65.17723	92.59337
district_id + cohort + period + enum_id + day_of_week	0.0334900	65.17885	92.59568
district_id + community_id + wave + cohort + enum_id + day_of_week	0.0334903	65.17946	92.59654
district_id + wave + cohort + enum_id + day_of_week	0.0334922	65.18302	92.60160
community_id + cohort + enum_id + on_time	0.0334943	65.18713	92.60744
community_id + wave + cohort + enum_id + on_time	0.0334954	65.18935	92.61059
district_id + community_id + cohort + enum_id + on_time	0.0334977	65.19376	92.61685
district_id + community_id + wave + cohort + enum_id + on_time	0.0334988	65.19593	92.61994
district_id + cohort + enum_id + day_of_week + on_time	0.0335055	65.20889	92.63836
wave + cohort + period + enum_id + day_of_week + on_time	0.0335144	65.22623	92.66299
wave + cohort + period + enum_id + day_of_week	0.0335183	65.23395	92.67395
district_id + wave + cohort + enum_id + on_time	0.0335215	65.24018	92.68280
district_id + cohort + enum_id	0.0335216	65.24030	92.68297
wave + cohort + enum_id + day_of_week + on_time	0.0335306	65.25776	92.70778
cohort + period + enum_id + day_of_week + on_time	0.0335336	65.26359	92.71606
district_id + cohort + enum_id + day_of_week	0.0335347	65.26588	92.71931
district_id + wave + cohort + period + enum_id	0.0335368	65.26982	92.72490
cohort + period + enum_id + day_of_week	0.0335371	65.27054	92.72593
district_id + wave + cohort + period + enum_id + on_time	0.0335468	65.28934	92.75263
wave + cohort + enum_id	0.0335479	65.29148	92.75569
district_id + cohort + enum_id + on_time	0.0335561	65.30739	92.77829
wave + cohort + enum_id + day_of_week	0.0335583	65.31176	92.78449
district_id + cohort + period + enum_id	0.0335601	65.31515	92.78931
district_id + cohort + period + enum_id + on_time	0.0335693	65.33306	92.81475
cohort + enum_id + day_of_week + on_time	0.0335730	65.34042	92.82521
cohort + enum_id	0.0335793	65.35262	92.84254
wave + cohort + enum_id + on_time	0.0335885	65.37046	92.86788
wave + cohort + period + enum_id	0.0335911	65.37551	92.87505
cohort + enum_id + day_of_week	0.0335999	65.39274	92.89954
wave + cohort + period + enum_id + on_time	0.0336029	65.39860	92.90786
cohort + period + enum_id	0.0336078	65.40810	92.92136
cohort + period + enum_id + on_time	0.0336188	65.42952	92.95179
cohort + enum_id + on_time	0.0336199	65.43153	92.95464
wave + on_time	0.0361525	70.36051	99.95694
wave + period + day_of_week + on_time	0.0361554	70.36632	99.96521
wave	0.0361574	70.37020	99.97072
wave + period + day_of_week	0.0361577	70.37079	99.97155
community_id + on_time	0.0361616	70.37823	99.98213
on_time	0.0361628	70.38056	99.98543
community_id + wave + on_time	0.0361628	70.38061	99.98550
district_id + community_id + on_time	0.0361652	70.38537	99.99226
district_id + community_id + wave + on_time	0.0361665	70.38775	99.99564
None	0.0361680	70.39082	100.00000
district_id + wave + on_time	0.0361690	70.39267	100.00263
district_id + wave	0.0361728	70.40002	100.01308
period + day_of_week + on_time	0.0361748	70.40402	100.01876
district_id + wave + period + day_of_week + on_time	0.0361764	70.40712	100.02316
period + day_of_week	0.0361772	70.40860	100.02526
district_id + wave + period + day_of_week	0.0361793	70.41283	100.03127
community_id + period + day_of_week + on_time	0.0361795	70.41309	100.03165
district_id + on_time	0.0361798	70.41365	100.03244
community_id + wave + period + day_of_week + on_time	0.0361807	70.41547	100.03503
district_id	0.0361830	70.41989	100.04131
district_id + community_id + period + day_of_week + on_time	0.0361831	70.42024	100.04180
district_id + community_id + wave + period + day_of_week + on_time	0.0361844	70.42262	100.04518
community_id	0.0361878	70.42935	100.05474
community_id + wave	0.0361890	70.43172	100.05812
district_id + community_id	0.0361915	70.43648	100.06488
district_id + community_id + wave	0.0361927	70.43887	100.06826
community_id + cohort + on_time	0.0361935	70.44038	100.07041
district_id + period + day_of_week + on_time	0.0361941	70.44154	100.07206
community_id + wave + cohort + on_time	0.0361947	70.44276	100.07379
district_id + period + day_of_week	0.0361970	70.44720	100.08010
district_id + community_id + cohort + on_time	0.0361972	70.44752	100.08055
district_id + community_id + wave + cohort + on_time	0.0361984	70.44990	100.08394
wave + day_of_week + on_time	0.0361987	70.45057	100.08489
community_id + period + day_of_week	0.0362084	70.46937	100.11159
community_id + wave + period + day_of_week	0.0362096	70.47175	100.11498
district_id + community_id + period + day_of_week	0.0362121	70.47652	100.12175
community_id + cohort	0.0362132	70.47869	100.12484
district_id + community_id + wave + period + day_of_week	0.0362133	70.47890	100.12514
community_id + wave + cohort	0.0362144	70.48107	100.12822
district_id + community_id + cohort	0.0362169	70.48584	100.13499
day_of_week + on_time	0.0362179	70.48786	100.13787
district_id + community_id + wave + cohort	0.0362181	70.48822	100.13838
district_id + wave + day_of_week + on_time	0.0362270	70.50562	100.16309
community_id + day_of_week + on_time	0.0362352	70.52146	100.18559
community_id + wave + day_of_week + on_time	0.0362364	70.52384	100.18898
district_id + community_id + day_of_week + on_time	0.0362388	70.52861	100.19576
district_id + community_id + wave + day_of_week + on_time	0.0362401	70.53100	100.19914
community_id + cohort + day_of_week + on_time	0.0362444	70.53941	100.21110
community_id + wave + cohort + day_of_week + on_time	0.0362456	70.54180	100.21449
district_id + day_of_week + on_time	0.0362457	70.54200	100.21477
district_id + community_id + cohort + day_of_week + on_time	0.0362481	70.54657	100.22126
community_id + cohort + period + day_of_week + on_time	0.0362487	70.54781	100.22303
district_id + community_id + wave + cohort + day_of_week + on_time	0.0362493	70.54895	100.22465
community_id + wave + cohort + period + day_of_week + on_time	0.0362499	70.55019	100.22642
district_id + community_id + cohort + period + day_of_week + on_time	0.0362524	70.55496	100.23319
district_id + community_id + wave + cohort + period + day_of_week + on_time	0.0362536	70.55735	100.23659
wave + period	0.0362564	70.56278	100.24430
wave + day_of_week	0.0362577	70.56539	100.24801
wave + period + on_time	0.0362630	70.57569	100.26264
period	0.0362680	70.58531	100.27631
district_id + wave + period	0.0362680	70.58533	100.27633
community_id + cohort + period + day_of_week	0.0362683	70.58606	100.27737
community_id + wave + cohort + period + day_of_week	0.0362696	70.58843	100.28074
district_id + community_id + cohort + period + day_of_week	0.0362720	70.59321	100.28753
district_id + community_id + wave + cohort + period + day_of_week	0.0362732	70.59560	100.29092
period + on_time	0.0362747	70.59845	100.29497
day_of_week	0.0362764	70.60167	100.29955
district_id + wave + period + on_time	0.0362769	70.60278	100.30113
community_id + period + on_time	0.0362776	70.60403	100.30290
community_id + wave + period + on_time	0.0362788	70.60641	100.30629
district_id + period	0.0362794	70.60754	100.30788
district_id + community_id + period + on_time	0.0362813	70.61119	100.31307
district_id + community_id + wave + period + on_time	0.0362825	70.61357	100.31646
district_id + wave + day_of_week	0.0362838	70.61620	100.32019
community_id + period	0.0362886	70.62556	100.33349
district_id + period + on_time	0.0362893	70.62677	100.33521
community_id + wave + period	0.0362899	70.62795	100.33688
district_id + community_id + period	0.0362923	70.63272	100.34366
district_id + community_id + wave + period	0.0362935	70.63511	100.34705
district_id + day_of_week	0.0363014	70.65032	100.36866
community_id + cohort + day_of_week	0.0363352	70.71613	100.46216
community_id + wave + cohort + day_of_week	0.0363364	70.71852	100.46556
community_id + cohort + period + on_time	0.0363370	70.71963	100.46712
community_id + wave + cohort + period + on_time	0.0363382	70.72202	100.47052
district_id + community_id + cohort + day_of_week	0.0363389	70.72331	100.47235
district_id + community_id + wave + cohort + day_of_week	0.0363401	70.72570	100.47575
district_id + community_id + cohort + period + on_time	0.0363407	70.72680	100.47731
district_id + community_id + wave + cohort + period + on_time	0.0363419	70.72919	100.48071
community_id + cohort + period	0.0363472	70.73950	100.49535
community_id + wave + cohort + period	0.0363484	70.74189	100.49875
district_id + community_id + cohort + period	0.0363509	70.74667	100.50554
district_id + community_id + wave + cohort + period	0.0363521	70.74906	100.50894
community_id + day_of_week	0.0363596	70.76358	100.52957
community_id + wave + day_of_week	0.0363608	70.76597	100.53296
district_id + community_id + day_of_week	0.0363632	70.77076	100.53976
district_id + community_id + wave + day_of_week	0.0363645	70.77315	100.54316
district_id + wave + cohort + period + day_of_week + on_time	0.0364603	70.95971	100.80820
district_id + wave + cohort + period + day_of_week	0.0364619	70.96267	100.81239
district_id + wave + cohort + on_time	0.0364655	70.96986	100.82261
district_id + wave + cohort	0.0364681	70.97477	100.82959
district_id + cohort + on_time	0.0364736	70.98544	100.84474
district_id + wave + cohort + day_of_week + on_time	0.0364736	70.98547	100.84479
district_id + cohort + period + day_of_week + on_time	0.0364751	70.98853	100.84914
district_id + cohort	0.0364756	70.98945	100.85045
district_id + cohort + period + day_of_week	0.0364766	70.99127	100.85303
district_id + cohort + day_of_week + on_time	0.0364937	71.02474	100.90058
district_id + wave + cohort + day_of_week	0.0365233	71.08232	100.98237
wave + cohort + period + day_of_week + on_time	0.0365313	71.09777	101.00433
wave + cohort + period + day_of_week	0.0365317	71.09857	101.00546
wave + cohort + day_of_week + on_time	0.0365352	71.10545	101.01524
district_id + cohort + day_of_week	0.0365418	71.11827	101.03345
wave + cohort + on_time	0.0365423	71.11926	101.03486
wave + cohort	0.0365449	71.12427	101.04198
cohort + period + day_of_week + on_time	0.0365532	71.14047	101.06498
cohort + period + day_of_week	0.0365535	71.14106	101.06583
cohort + on_time	0.0365554	71.14472	101.07103
cohort	0.0365584	71.15057	101.07934
cohort + day_of_week + on_time	0.0365633	71.16015	101.09295
district_id + wave + cohort + period	0.0365675	71.16820	101.10438
district_id + wave + cohort + period + on_time	0.0365744	71.18172	101.12359
district_id + cohort + period	0.0365755	71.18382	101.12657
district_id + cohort + period + on_time	0.0365832	71.19891	101.14801
wave + cohort + day_of_week	0.0365862	71.20470	101.15624
cohort + day_of_week	0.0366131	71.25711	101.23069
wave + cohort + period	0.0366493	71.32750	101.33069
wave + cohort + period + on_time	0.0366551	71.33881	101.34676
cohort + period	0.0366630	71.35405	101.36840
cohort + period + on_time	0.0366688	71.36537	101.38449

Total Consumption

```{r}
#| warning: false
#| message: false
#| label: tbl-cons-ses
#| classes: plain

consumption_power_set_se %>%
    nice_table()
```

FE Specification	Average SE	As % of Coef.	As % of No FE SE
district_id + wave + period + enum_id + on_time	18.94072	38.27219	95.25618
district_id + wave + period + enum_id	18.94571	38.28227	95.28128
district_id + period + enum_id + on_time	18.95151	38.29399	95.31045
district_id + wave + cohort + period + enum_id + on_time	18.95244	38.29586	95.31510
district_id + wave + cohort + period + enum_id	18.95461	38.30025	95.32602
district_id + period + enum_id	18.95688	38.30483	95.33743
wave + period + enum_id + on_time	18.95763	38.30634	95.34119
district_id + cohort + period + enum_id + on_time	18.95896	38.30904	95.34791
period + enum_id + on_time	18.96014	38.31143	95.35384
district_id + cohort + period + enum_id	18.96150	38.31416	95.36065
wave + cohort + period + enum_id + on_time	18.96445	38.32012	95.37549
wave + period + enum_id	18.96452	38.32028	95.37587
cohort + period + enum_id + on_time	18.96501	38.32126	95.37832
wave + cohort + period + enum_id	18.96777	38.32683	95.39218
period + enum_id	18.96792	38.32714	95.39294
cohort + period + enum_id	18.96921	38.32976	95.39947
district_id + wave + period + enum_id + day_of_week	18.98679	38.36526	95.48783
district_id + wave + cohort + period + enum_id + day_of_week	18.99093	38.37363	95.50866
district_id + period + enum_id + day_of_week	18.99642	38.38472	95.53627
district_id + cohort + period + enum_id + day_of_week	18.99652	38.38493	95.53678
district_id + wave + period + enum_id + day_of_week + on_time	18.99999	38.39193	95.55422
cohort + period + enum_id + day_of_week	19.00037	38.39272	95.55618
wave + cohort + period + enum_id + day_of_week	19.00185	38.39571	95.56362
wave + period + enum_id + day_of_week	19.00268	38.39739	95.56779
period + enum_id + day_of_week	19.00279	38.39760	95.56833
district_id + wave + cohort + period + enum_id + day_of_week + on_time	19.00639	38.40487	95.58641
district_id + period + enum_id + day_of_week + on_time	19.01008	38.41233	95.60498
district_id + cohort + period + enum_id + day_of_week + on_time	19.01263	38.41748	95.61780
wave + period + enum_id + day_of_week + on_time	19.01536	38.42299	95.63153
period + enum_id + day_of_week + on_time	19.01561	38.42351	95.63280
cohort + period + enum_id + day_of_week + on_time	19.01590	38.42408	95.63423
wave + cohort + period + enum_id + day_of_week + on_time	19.01708	38.42648	95.64021
community_id + period + enum_id	19.06285	38.51895	95.87035
community_id + wave + period + enum_id	19.06349	38.52025	95.87360
district_id + community_id + period + enum_id	19.06478	38.52285	95.88006
district_id + community_id + wave + period + enum_id	19.06543	38.52417	95.88334
community_id + period + enum_id + on_time	19.07193	38.53732	95.91606
community_id + wave + period + enum_id + on_time	19.07258	38.53862	95.91930
district_id + community_id + period + enum_id + on_time	19.07387	38.54124	95.92582
district_id + community_id + wave + period + enum_id + on_time	19.07452	38.54254	95.92907
community_id + cohort + period + enum_id	19.11260	38.61948	96.12056
community_id + wave + cohort + period + enum_id	19.11325	38.62080	96.12384
district_id + community_id + cohort + period + enum_id	19.11455	38.62343	96.13040
district_id + community_id + wave + cohort + period + enum_id	19.11520	38.62474	96.13366
community_id + period + enum_id + day_of_week	19.11568	38.62570	96.13605
community_id + wave + period + enum_id + day_of_week	19.11634	38.62704	96.13937
district_id + community_id + period + enum_id + day_of_week	19.11762	38.62964	96.14584
district_id + community_id + wave + period + enum_id + day_of_week	19.11827	38.63095	96.14911
community_id + cohort + period + enum_id + on_time	19.12489	38.64433	96.18241
community_id + wave + cohort + period + enum_id + on_time	19.12555	38.64565	96.18569
district_id + community_id + cohort + period + enum_id + on_time	19.12685	38.64828	96.19223
district_id + community_id + wave + cohort + period + enum_id + on_time	19.12750	38.64959	96.19550
community_id + period + enum_id + day_of_week + on_time	19.13446	38.66365	96.23050
community_id + wave + period + enum_id + day_of_week + on_time	19.13511	38.66498	96.23381
district_id + community_id + period + enum_id + day_of_week + on_time	19.13641	38.66759	96.24030
district_id + community_id + wave + period + enum_id + day_of_week + on_time	19.13705	38.66889	96.24355
community_id + cohort + period + enum_id + day_of_week	19.16731	38.73003	96.39572
community_id + wave + cohort + period + enum_id + day_of_week	19.16796	38.73135	96.39899
district_id + community_id + cohort + period + enum_id + day_of_week	19.16927	38.73399	96.40557
district_id + community_id + wave + cohort + period + enum_id + day_of_week	19.16991	38.73529	96.40881
community_id + cohort + period + enum_id + day_of_week + on_time	19.18922	38.77430	96.50590
community_id + wave + cohort + period + enum_id + day_of_week + on_time	19.18987	38.77561	96.50917
district_id + community_id + cohort + period + enum_id + day_of_week + on_time	19.19118	38.77827	96.51578
district_id + community_id + wave + cohort + period + enum_id + day_of_week + on_time	19.19183	38.77958	96.51903
district_id + wave + enum_id	19.30085	38.99988	97.06734
district_id + enum_id	19.30296	39.00414	97.07794
district_id + cohort + enum_id	19.30622	39.01071	97.09431
district_id + wave + cohort + enum_id	19.30645	39.01119	97.09550
district_id + wave + enum_id + on_time	19.31715	39.03281	97.14931
district_id + enum_id + on_time	19.31855	39.03564	97.15636
district_id + cohort + enum_id + on_time	19.31928	39.03712	97.16003
district_id + wave + cohort + enum_id + on_time	19.32036	39.03929	97.16543
community_id + enum_id	19.33127	39.06134	97.22031
community_id + wave + enum_id	19.33192	39.06265	97.22358
district_id + community_id + enum_id	19.33324	39.06531	97.23019
district_id + community_id + wave + enum_id	19.33389	39.06663	97.23348
cohort + enum_id	19.33745	39.07382	97.25137
enum_id	19.33932	39.07760	97.26078
wave + cohort + enum_id	19.34443	39.08793	97.28649
community_id + enum_id + on_time	19.34573	39.09054	97.29300
wave + enum_id	19.34594	39.09099	97.29410
community_id + wave + enum_id + on_time	19.34638	39.09187	97.29631
cohort + enum_id + on_time	19.34701	39.09315	97.29948
district_id + community_id + enum_id + on_time	19.34769	39.09452	97.30291
district_id + community_id + wave + enum_id + on_time	19.34835	39.09585	97.30621
enum_id + on_time	19.35165	39.10252	97.32281
wave + cohort + enum_id + on_time	19.35485	39.10897	97.33887
wave + enum_id + on_time	19.35908	39.11753	97.36016
community_id + cohort + enum_id	19.37139	39.14240	97.42207
community_id + wave + cohort + enum_id	19.37205	39.14373	97.42537
district_id + community_id + cohort + enum_id	19.37336	39.14639	97.43199
district_id + community_id + wave + cohort + enum_id	19.37402	39.14771	97.43528
community_id + cohort + enum_id + on_time	19.37874	39.15726	97.45905
community_id + wave + cohort + enum_id + on_time	19.37940	39.15859	97.46235
district_id + community_id + cohort + enum_id + on_time	19.38072	39.16125	97.46898
district_id + community_id + wave + cohort + enum_id + on_time	19.38137	39.16257	97.47228
district_id + cohort + enum_id + day_of_week	19.40555	39.21142	97.59385
district_id + wave + cohort + enum_id + day_of_week	19.41061	39.22165	97.61931
district_id + cohort + enum_id + day_of_week + on_time	19.42079	39.24222	97.67050
district_id + enum_id + day_of_week	19.42545	39.25164	97.69396
district_id + wave + cohort + enum_id + day_of_week + on_time	19.42573	39.25220	97.69534
cohort + enum_id + day_of_week	19.42637	39.25350	97.69859
district_id + wave + enum_id + day_of_week	19.42863	39.25806	97.70994
district_id + enum_id + day_of_week + on_time	19.43728	39.27554	97.75344
wave + cohort + enum_id + day_of_week	19.43819	39.27739	97.75805
district_id + wave + enum_id + day_of_week + on_time	19.44052	39.28209	97.76973
cohort + enum_id + day_of_week + on_time	19.44169	39.28446	97.77563
community_id + enum_id + day_of_week	19.44569	39.29254	97.79575
community_id + wave + enum_id + day_of_week	19.44635	39.29387	97.79907
district_id + community_id + enum_id + day_of_week	19.44767	39.29654	97.80572
district_id + community_id + wave + enum_id + day_of_week	19.44833	39.29787	97.80902
wave + cohort + enum_id + day_of_week + on_time	19.45368	39.30869	97.83594
enum_id + day_of_week	19.45373	39.30877	97.83615
enum_id + day_of_week + on_time	19.46528	39.33213	97.89429
wave + enum_id + day_of_week	19.46573	39.33304	97.89655
community_id + cohort + enum_id + day_of_week	19.46664	39.33488	97.90113
community_id + wave + cohort + enum_id + day_of_week	19.46730	39.33621	97.90445
community_id + enum_id + day_of_week + on_time	19.46822	39.33805	97.90903
district_id + community_id + cohort + enum_id + day_of_week	19.46863	39.33889	97.91110
community_id + wave + enum_id + day_of_week + on_time	19.46888	39.33939	97.91237
district_id + community_id + wave + cohort + enum_id + day_of_week	19.46929	39.34022	97.91442
district_id + community_id + enum_id + day_of_week + on_time	19.47020	39.34207	97.91902
district_id + community_id + wave + enum_id + day_of_week + on_time	19.47086	39.34340	97.92233
wave + enum_id + day_of_week + on_time	19.47758	39.35697	97.95611
community_id + cohort + enum_id + day_of_week + on_time	19.49503	39.39223	98.04388
community_id + wave + cohort + enum_id + day_of_week + on_time	19.49568	39.39356	98.04717
district_id + community_id + cohort + enum_id + day_of_week + on_time	19.49701	39.39624	98.05384
district_id + community_id + wave + cohort + enum_id + day_of_week + on_time	19.49767	39.39757	98.05717
district_id + wave + period + on_time	19.79325	39.99482	99.54366
wave + cohort + period + on_time	19.79572	39.99982	99.55612
district_id + wave + period	19.79778	40.00399	99.56648
wave + cohort + period	19.79814	40.00470	99.56826
district_id + period + on_time	19.80264	40.01381	99.59092
cohort + period + on_time	19.80281	40.01415	99.59177
cohort + period	19.80576	40.02010	99.60659
wave + period + on_time	19.80634	40.02129	99.60953
district_id + wave + cohort + period + on_time	19.80735	40.02332	99.61461
community_id + period	19.80738	40.02339	99.61476
district_id + wave + cohort + period	19.80749	40.02361	99.61532
district_id + period	19.80761	40.02383	99.61588
community_id + wave + period	19.80805	40.02473	99.61812
period + on_time	19.80934	40.02735	99.62463
district_id + community_id + period	19.80938	40.02743	99.62482
district_id + community_id + wave + period	19.81005	40.02878	99.62818
district_id + cohort + period + on_time	19.81465	40.03807	99.65131
district_id + cohort + period	19.81521	40.03919	99.65410
wave + period	19.81639	40.04158	99.66004
community_id + period + on_time	19.81714	40.04310	99.66382
community_id + wave + period + on_time	19.81781	40.04445	99.66718
district_id + community_id + period + on_time	19.81914	40.04714	99.67389
district_id + community_id + wave + period + on_time	19.81981	40.04849	99.67725
period	19.82009	40.04907	99.67868
cohort + period + day_of_week	19.84007	40.08944	99.77916
wave + cohort + period + day_of_week	19.84188	40.09310	99.78827
cohort + period + day_of_week + on_time	19.85300	40.11556	99.84417
district_id + wave + period + day_of_week	19.85373	40.11704	99.84787
wave + cohort + period + day_of_week + on_time	19.85528	40.12017	99.85566
district_id + wave + cohort + period + day_of_week	19.85566	40.12093	99.85754
community_id + cohort + period	19.85667	40.12297	99.86263
community_id + wave + cohort + period	19.85734	40.12432	99.86599
district_id + community_id + cohort + period	19.85867	40.12703	99.87272
district_id + cohort + period + day_of_week	19.85871	40.12710	99.87290
district_id + period + day_of_week	19.85874	40.12717	99.87306
community_id + period + day_of_week	19.85909	40.12787	99.87482
district_id + community_id + wave + cohort + period	19.85934	40.12838	99.87608
wave + cohort	19.85957	40.12883	99.87720
community_id + wave + period + day_of_week	19.85976	40.12922	99.87818
district_id + community_id + period + day_of_week	19.86110	40.13193	99.88491
district_id + wave + period + day_of_week + on_time	19.86162	40.13298	99.88754
district_id + community_id + wave + period + day_of_week	19.86177	40.13328	99.88828
period + day_of_week	19.86202	40.13378	99.88953
district_id + period + day_of_week + on_time	19.86659	40.14302	99.91252
cohort	19.86664	40.14313	99.91279
period + day_of_week + on_time	19.86766	40.14519	99.91792
wave + period + day_of_week	19.86864	40.14716	99.92282
district_id + wave + cohort + period + day_of_week + on_time	19.86896	40.14782	99.92446
community_id + cohort + period + on_time	19.87131	40.15255	99.93625
community_id + wave + cohort + period + on_time	19.87198	40.15390	99.93961
district_id + cohort + period + day_of_week + on_time	19.87226	40.15448	99.94105
district_id + community_id + cohort + period + on_time	19.87331	40.15661	99.94634
district_id + community_id + wave + cohort + period + on_time	19.87398	40.15796	99.94971
wave + period + day_of_week + on_time	19.87492	40.15985	99.95441
community_id + period + day_of_week + on_time	19.87895	40.16800	99.97469
community_id + wave + period + day_of_week + on_time	19.87962	40.16935	99.97805
district_id + community_id + period + day_of_week + on_time	19.88096	40.17205	99.98479
wave	19.88122	40.17259	99.98611
district_id + community_id + wave + period + day_of_week + on_time	19.88163	40.17341	99.98815
wave + cohort + on_time	19.88277	40.17571	99.99388
None	19.88398	40.17817	100.00000
community_id	19.88723	40.18472	100.01631
community_id + wave	19.88790	40.18607	100.01968
district_id + wave	19.88873	40.18776	100.02387
district_id + community_id	19.88923	40.18878	100.02641
cohort + on_time	19.88930	40.18891	100.02673
district_id + community_id + wave	19.88990	40.19013	100.02977
district_id + wave + cohort	19.89434	40.19908	100.05206
district_id	19.89723	40.20494	100.06663
district_id + cohort	19.90148	40.21351	100.08798
wave + on_time	19.90309	40.21678	100.09609
on_time	19.90524	40.22111	100.10688
community_id + cohort + period + day_of_week	19.91008	40.23089	100.13122
community_id + wave + cohort + period + day_of_week	19.91075	40.23224	100.13459
district_id + community_id + cohort + period + day_of_week	19.91209	40.23495	100.14133
district_id + community_id + wave + cohort + period + day_of_week	19.91276	40.23631	100.14471
district_id + wave + on_time	19.91519	40.24122	100.15694
community_id + on_time	19.91720	40.24529	100.16707
community_id + wave + on_time	19.91787	40.24665	100.17044
district_id + community_id + on_time	19.91921	40.24935	100.17718
district_id + wave + cohort + on_time	19.91951	40.24996	100.17869
district_id + community_id + wave + on_time	19.91988	40.25071	100.18055
district_id + on_time	19.92318	40.25736	100.19711
district_id + cohort + on_time	19.92603	40.26312	100.21144
community_id + cohort + period + day_of_week + on_time	19.93685	40.28498	100.26586
community_id + wave + cohort + period + day_of_week + on_time	19.93752	40.28634	100.26924
district_id + community_id + cohort + period + day_of_week + on_time	19.93886	40.28906	100.27599
district_id + community_id + wave + cohort + period + day_of_week + on_time	19.93953	40.29041	100.27937
community_id + cohort	19.94346	40.29835	100.29912
community_id + wave + cohort	19.94413	40.29971	100.30250
district_id + community_id + cohort	19.94547	40.30242	100.30925
district_id + community_id + wave + cohort	19.94615	40.30377	100.31263
community_id + cohort + on_time	19.97026	40.35251	100.43392
community_id + wave + cohort + on_time	19.97094	40.35386	100.43730
district_id + community_id + cohort + on_time	19.97228	40.35658	100.44406
district_id + community_id + wave + cohort + on_time	19.97295	40.35794	100.44744
cohort + day_of_week	20.07088	40.55582	100.93994
wave + cohort + day_of_week	20.08610	40.58656	101.01646
cohort + day_of_week + on_time	20.13131	40.67792	101.24384
district_id + cohort + day_of_week	20.14361	40.70278	101.30571
day_of_week	20.14821	40.71206	101.32882
district_id + wave + cohort + day_of_week	20.14826	40.71217	101.32908
wave + cohort + day_of_week + on_time	20.14921	40.71410	101.33388
community_id + day_of_week	20.16147	40.73887	101.39554
community_id + wave + day_of_week	20.16215	40.74024	101.39895
district_id + community_id + day_of_week	20.16351	40.74298	101.40578
district_id + community_id + wave + day_of_week	20.16419	40.74436	101.40920
wave + day_of_week	20.16749	40.75103	101.42580
community_id + cohort + day_of_week	20.17186	40.75986	101.44779
community_id + wave + cohort + day_of_week	20.17254	40.76124	101.45121
district_id + community_id + cohort + day_of_week	20.17390	40.76398	101.45804
district_id + community_id + wave + cohort + day_of_week	20.17458	40.76535	101.46146
day_of_week + on_time	20.18331	40.78300	101.50539
district_id + day_of_week	20.19077	40.79807	101.54288
district_id + wave + day_of_week	20.19306	40.80271	101.55442
district_id + cohort + day_of_week + on_time	20.20007	40.81686	101.58965
wave + day_of_week + on_time	20.20582	40.82848	101.61857
district_id + wave + cohort + day_of_week + on_time	20.20607	40.82898	101.61982
district_id + day_of_week + on_time	20.22750	40.87228	101.72759
district_id + wave + day_of_week + on_time	20.23200	40.88138	101.75024
community_id + day_of_week + on_time	20.23762	40.89273	101.77847
community_id + wave + day_of_week + on_time	20.23830	40.89410	101.78190
district_id + community_id + day_of_week + on_time	20.23966	40.89686	101.78876
district_id + community_id + wave + day_of_week + on_time	20.24034	40.89823	101.79218
community_id + cohort + day_of_week + on_time	20.27805	40.97442	101.98182
community_id + wave + cohort + day_of_week + on_time	20.27873	40.97580	101.98525
district_id + community_id + cohort + day_of_week + on_time	20.28010	40.97856	101.99212
district_id + community_id + wave + cohort + day_of_week + on_time	20.28078	40.97994	101.99555

Total Income

```{r}
#| warning: false
#| message: false
#| label: tbl-inc-ses
#| classes: plain

income_power_set_se %>%
    nice_table()
```

FE Specification	Average SE	As % of Coef.	As % of No FE SE
district_id + wave + cohort	10.69914	47.21249	97.73730
district_id + wave + cohort + period	10.70116	47.22141	97.75575
district_id + cohort	10.71260	47.27188	97.86025
district_id + cohort + period	10.71463	47.28081	97.87872
district_id + wave	10.80290	47.67035	98.68513
district_id + wave + period	10.80494	47.67935	98.70376
district_id	10.81620	47.72903	98.80661
district_id + period	10.81824	47.73804	98.82526
wave + cohort	10.82198	47.75453	98.85939
wave + cohort + period	10.82402	47.76354	98.87805
district_id + wave + cohort + period + enum_id	10.83839	47.82693	99.00928
cohort	10.84102	47.83855	99.03334
district_id + cohort + period + enum_id	10.84159	47.84106	99.03853
cohort + period	10.84307	47.84758	99.05203
district_id + wave + period + enum_id	10.87625	47.99401	99.35517
wave + cohort + period + enum_id	10.87818	48.00251	99.37276
district_id + period + enum_id	10.87824	48.00280	99.37336
cohort + period + enum_id	10.88899	48.05025	99.47159
wave + period + enum_id	10.92290	48.19985	99.78129
wave	10.92671	48.21667	99.81611
wave + period	10.92877	48.22577	99.83495
period + enum_id	10.93296	48.24425	99.87320
None	10.94684	48.30550	100.00000
period	10.94890	48.31462	100.01887
district_id + wave + cohort + enum_id	11.03892	48.71181	100.84113
district_id + cohort + enum_id	11.04425	48.73535	100.88985
community_id + cohort	11.06183	48.81293	101.05046
community_id + wave + cohort	11.06218	48.81447	101.05364
district_id + community_id + cohort	11.06287	48.81754	101.05999
district_id + community_id + wave + cohort	11.06322	48.81907	101.06317
community_id + cohort + period	11.06392	48.82214	101.06953
community_id + wave + cohort + period	11.06427	48.82368	101.07271
district_id + community_id + cohort + period	11.06496	48.82675	101.07907
district_id + community_id + wave + cohort + period	11.06531	48.82829	101.08225
wave + cohort + enum_id	11.07607	48.87576	101.18053
district_id + wave + enum_id	11.08287	48.90576	101.24263
district_id + enum_id	11.08715	48.92465	101.28173
cohort + enum_id	11.09070	48.94035	101.31423
community_id	11.09726	48.96929	101.37415
community_id + wave	11.09761	48.97083	101.37734
district_id + community_id	11.09831	48.97391	101.38372
district_id + community_id + wave	11.09866	48.97545	101.38691
community_id + period	11.09936	48.97854	101.39329
community_id + wave + period	11.09971	48.98008	101.39648
district_id + community_id + period	11.10041	48.98316	101.40286
district_id + community_id + wave + period	11.10076	48.98470	101.40605
wave + enum_id	11.12581	49.09526	101.63493
community_id + cohort + period + enum_id	11.13088	49.11765	101.68127
community_id + wave + cohort + period + enum_id	11.13124	49.11920	101.68449
district_id + community_id + cohort + period + enum_id	11.13194	49.12231	101.69093
district_id + community_id + wave + cohort + period + enum_id	11.13229	49.12387	101.69415
enum_id	11.14003	49.15800	101.76481
community_id + period + enum_id	11.16232	49.25634	101.96839
community_id + wave + period + enum_id	11.16267	49.25790	101.97162
district_id + community_id + period + enum_id	11.16338	49.26102	101.97808
district_id + community_id + wave + period + enum_id	11.16373	49.26258	101.98131
community_id + cohort + enum_id	11.31381	49.92483	103.35227
community_id + wave + cohort + enum_id	11.31416	49.92641	103.35554
district_id + community_id + cohort + enum_id	11.31488	49.92958	103.36209
district_id + community_id + wave + cohort + enum_id	11.31524	49.93116	103.36536
community_id + enum_id	11.35082	50.08815	103.69036
community_id + wave + enum_id	11.35117	50.08973	103.69364
district_id + community_id + enum_id	11.35189	50.09290	103.70020
district_id + community_id + wave + enum_id	11.35225	50.09449	103.70349
district_id + wave + cohort + period + on_time	11.52603	50.86132	105.29094
district_id + cohort + period + on_time	11.53261	50.89036	105.35107
district_id + wave + cohort + on_time	11.56380	51.02799	105.63598
district_id + cohort + on_time	11.56921	51.05186	105.68539
district_id + wave + cohort + period + day_of_week + on_time	11.58594	51.12568	105.83822
district_id + wave + cohort + period + day_of_week	11.59006	51.14386	105.87585
district_id + cohort + period + day_of_week + on_time	11.59179	51.15148	105.89163
district_id + cohort + period + day_of_week	11.59568	51.16867	105.92721
district_id + wave + period + on_time	11.61384	51.24881	106.09310
district_id + period + on_time	11.61938	51.27326	106.14373
district_id + wave + cohort + day_of_week	11.62712	51.30741	106.21443
wave + cohort + period + on_time	11.62845	51.31327	106.22655
cohort + period + on_time	11.63430	51.33910	106.28003
district_id + cohort + day_of_week	11.63497	51.34206	106.28615
district_id + wave + cohort + day_of_week + on_time	11.64930	51.40528	106.41702
district_id + wave + on_time	11.65103	51.41291	106.43283
district_id + on_time	11.65560	51.43309	106.47461
district_id + cohort + day_of_week + on_time	11.65634	51.43636	106.48136
wave + cohort + on_time	11.65804	51.44383	106.49684
cohort + on_time	11.66328	51.46699	106.54477
district_id + wave + cohort + period + enum_id + on_time	11.66756	51.48586	106.58385
district_id + cohort + period + enum_id + on_time	11.67491	51.51828	106.65095
district_id + wave + period + day_of_week + on_time	11.67882	51.53556	106.68674
district_id + wave + period + day_of_week	11.68271	51.55273	106.72226
district_id + period + day_of_week + on_time	11.68338	51.55566	106.72835
district_id + period + day_of_week	11.68697	51.57151	106.76115
district_id + wave + cohort + period + enum_id + day_of_week + on_time	11.68824	51.57711	106.77275
district_id + wave + cohort + period + enum_id + day_of_week	11.68979	51.58393	106.78687
wave + cohort + period + day_of_week + on_time	11.69551	51.60918	106.83914
district_id + cohort + period + enum_id + day_of_week + on_time	11.69641	51.61316	106.84738
wave + cohort + period + day_of_week	11.69659	51.61395	106.84900
district_id + cohort + period + enum_id + day_of_week	11.69785	51.61950	106.86050
cohort + period + day_of_week + on_time	11.70070	51.63210	106.88659
cohort + period + day_of_week	11.70156	51.63590	106.89445
district_id + wave + period + enum_id + on_time	11.71130	51.67887	106.98340
district_id + period + enum_id + on_time	11.71583	51.69886	107.02479
wave + period + on_time	11.71851	51.71069	107.04927
period + on_time	11.72222	51.72705	107.08315
wave + cohort + day_of_week	11.72304	51.73069	107.09068
district_id + wave + day_of_week	11.72326	51.73163	107.09264
district_id + day_of_week	11.72937	51.75860	107.14847
cohort + day_of_week	11.73027	51.76257	107.15668
district_id + wave + period + enum_id + day_of_week + on_time	11.73543	51.78535	107.20383
district_id + wave + period + enum_id + day_of_week	11.73712	51.79280	107.21926
wave + cohort + period + enum_id + on_time	11.73799	51.79664	107.22721
district_id + period + enum_id + day_of_week + on_time	11.74063	51.80827	107.25129
district_id + period + enum_id + day_of_week	11.74222	51.81532	107.26587
district_id + wave + day_of_week + on_time	11.74238	51.81602	107.26733
wave + cohort + day_of_week + on_time	11.74321	51.81968	107.27491
wave + on_time	11.74713	51.83696	107.31068
district_id + day_of_week + on_time	11.74767	51.83935	107.31562
cohort + day_of_week + on_time	11.74918	51.84603	107.32945
on_time	11.75061	51.85234	107.34251
cohort + period + enum_id + on_time	11.75614	51.87673	107.39300
wave + cohort + period + enum_id + day_of_week	11.75780	51.88406	107.40817
wave + cohort + period + enum_id + day_of_week + on_time	11.75836	51.88652	107.41327
cohort + period + enum_id + day_of_week	11.77682	51.96799	107.58192
cohort + period + enum_id + day_of_week + on_time	11.77760	51.97145	107.58909
wave + period + enum_id + on_time	11.78963	52.02452	107.69896
wave + period + day_of_week + on_time	11.79215	52.03564	107.72198
wave + period + day_of_week	11.79275	52.03830	107.72749
period + day_of_week + on_time	11.79437	52.04542	107.74221
period + day_of_week	11.79462	52.04654	107.74453
period + enum_id + on_time	11.80491	52.09196	107.83856
wave + period + enum_id + day_of_week	11.81283	52.12690	107.91089
wave + period + enum_id + day_of_week + on_time	11.81342	52.12952	107.91631
wave + day_of_week	11.82378	52.17521	108.01091
day_of_week	11.82739	52.19114	108.04387
period + enum_id + day_of_week	11.82861	52.19651	108.05500
period + enum_id + day_of_week + on_time	11.82942	52.20012	108.06247
wave + day_of_week + on_time	11.83974	52.24566	108.15674
day_of_week + on_time	11.84223	52.25662	108.17944
district_id + wave + cohort + enum_id + on_time	11.90616	52.53875	108.76349
district_id + wave + cohort + enum_id + day_of_week	11.90718	52.54323	108.77277
district_id + wave + cohort + enum_id + day_of_week + on_time	11.91063	52.55845	108.80427
district_id + cohort + enum_id + on_time	11.91571	52.58087	108.85070
district_id + cohort + enum_id + day_of_week	11.91865	52.59384	108.87754
district_id + cohort + enum_id + day_of_week + on_time	11.92193	52.60832	108.90751
community_id + cohort + period + on_time	11.92438	52.61913	108.92989
community_id + wave + cohort + period + on_time	11.92478	52.62090	108.93355
district_id + community_id + cohort + period + on_time	11.92558	52.62444	108.94089
district_id + community_id + wave + cohort + period + on_time	11.92598	52.62622	108.94456
district_id + wave + enum_id + on_time	11.95573	52.75749	109.21631
community_id + period + on_time	11.95818	52.76830	109.23870
community_id + wave + period + on_time	11.95859	52.77008	109.24237
community_id + cohort + period + day_of_week + on_time	11.95924	52.77296	109.24834
district_id + community_id + period + on_time	11.95939	52.77363	109.24973
community_id + wave + cohort + period + day_of_week + on_time	11.95964	52.77474	109.25203
district_id + community_id + wave + period + on_time	11.95979	52.77541	109.25341
district_id + community_id + cohort + period + day_of_week + on_time	11.96045	52.77829	109.25939
district_id + community_id + wave + cohort + period + day_of_week + on_time	11.96085	52.78007	109.26307
district_id + enum_id + on_time	11.96264	52.78798	109.27943
district_id + wave + enum_id + day_of_week	11.96297	52.78942	109.28242
community_id + cohort + on_time	11.96471	52.79710	109.29832
community_id + wave + cohort + on_time	11.96511	52.79888	109.30200
district_id + community_id + cohort + on_time	11.96592	52.80243	109.30936
district_id + wave + enum_id + day_of_week + on_time	11.96597	52.80267	109.30985
district_id + community_id + wave + cohort + on_time	11.96632	52.80421	109.31304
community_id + cohort + period + day_of_week	11.96937	52.81766	109.34088
community_id + wave + cohort + period + day_of_week	11.96977	52.81943	109.34455
district_id + community_id + cohort + period + day_of_week	11.97058	52.82299	109.35192
district_id + community_id + wave + cohort + period + day_of_week	11.97098	52.82477	109.35560
district_id + enum_id + day_of_week	11.97124	52.82593	109.35800
district_id + enum_id + day_of_week + on_time	11.97410	52.83855	109.38412
wave + cohort + enum_id + on_time	11.97626	52.84807	109.40384
wave + cohort + enum_id + day_of_week	11.97859	52.85835	109.42512
community_id + cohort + day_of_week	11.97999	52.86453	109.43792
community_id + wave + cohort + day_of_week	11.98039	52.86631	109.44159
district_id + community_id + cohort + day_of_week	11.98120	52.86987	109.44896
district_id + community_id + wave + cohort + day_of_week	11.98160	52.87165	109.45265
wave + cohort + enum_id + day_of_week + on_time	11.98237	52.87505	109.45968
community_id + cohort + period + enum_id + on_time	11.99374	52.92522	109.56355
community_id + period + day_of_week + on_time	11.99389	52.92587	109.56489
community_id + wave + cohort + period + enum_id + on_time	11.99415	52.92702	109.56727
community_id + wave + period + day_of_week + on_time	11.99429	52.92765	109.56857
district_id + community_id + cohort + period + enum_id + on_time	11.99496	52.93061	109.57469
district_id + community_id + period + day_of_week + on_time	11.99510	52.93121	109.57595
district_id + community_id + wave + cohort + period + enum_id + on_time	11.99537	52.93240	109.57841
district_id + community_id + wave + period + day_of_week + on_time	11.99551	52.93300	109.57964
community_id + on_time	11.99734	52.94110	109.59643
community_id + wave + on_time	11.99775	52.94289	109.60011
district_id + community_id + on_time	11.99855	52.94645	109.60749
district_id + community_id + wave + on_time	11.99896	52.94823	109.61118
cohort + enum_id + on_time	11.99988	52.95230	109.61960
community_id + cohort + period + enum_id + day_of_week + on_time	12.00005	52.95304	109.62114
community_id + wave + cohort + period + enum_id + day_of_week + on_time	12.00046	52.95484	109.62485
district_id + community_id + cohort + period + enum_id + day_of_week + on_time	12.00127	52.95843	109.63230
district_id + community_id + wave + cohort + period + enum_id + day_of_week + on_time	12.00168	52.96023	109.63601
community_id + period + day_of_week	12.00352	52.96836	109.65285
community_id + wave + period + day_of_week	12.00393	52.97015	109.65655
district_id + community_id + period + day_of_week	12.00473	52.97371	109.66393
district_id + community_id + wave + period + day_of_week	12.00514	52.97550	109.66763
cohort + enum_id + day_of_week	12.00516	52.97560	109.66784
community_id + cohort + period + enum_id + day_of_week	12.00535	52.97642	109.66954
community_id + wave + cohort + period + enum_id + day_of_week	12.00576	52.97822	109.67327
district_id + community_id + cohort + period + enum_id + day_of_week	12.00657	52.98183	109.68073
district_id + community_id + wave + cohort + period + enum_id + day_of_week	12.00698	52.98362	109.68444
cohort + enum_id + day_of_week + on_time	12.00873	52.99137	109.70048
community_id + cohort + day_of_week + on_time	12.01104	53.00156	109.72157
community_id + wave + cohort + day_of_week + on_time	12.01145	53.00334	109.72526
district_id + community_id + cohort + day_of_week + on_time	12.01226	53.00691	109.73266
district_id + community_id + wave + cohort + day_of_week + on_time	12.01266	53.00870	109.73636
community_id + day_of_week	12.02210	53.05033	109.82254
community_id + wave + day_of_week	12.02250	53.05212	109.82624
district_id + community_id + day_of_week	12.02331	53.05569	109.83363
district_id + community_id + wave + day_of_week	12.02372	53.05747	109.83733
wave + enum_id + on_time	12.03254	53.09643	109.91798
community_id + period + enum_id + on_time	12.03613	53.11227	109.95077
community_id + wave + period + enum_id + on_time	12.03654	53.11407	109.95449
district_id + community_id + period + enum_id + on_time	12.03736	53.11767	109.96195
district_id + community_id + wave + period + enum_id + on_time	12.03776	53.11947	109.96568
wave + enum_id + day_of_week	12.04147	53.13584	109.99956
community_id + period + enum_id + day_of_week + on_time	12.04318	53.14336	110.01513
community_id + wave + period + enum_id + day_of_week + on_time	12.04359	53.14517	110.01887
district_id + community_id + period + enum_id + day_of_week + on_time	12.04440	53.14877	110.02632
wave + enum_id + day_of_week + on_time	12.04477	53.15040	110.02969
district_id + community_id + wave + period + enum_id + day_of_week + on_time	12.04481	53.15057	110.03005
community_id + period + enum_id + day_of_week	12.04798	53.16455	110.05900
community_id + wave + period + enum_id + day_of_week	12.04839	53.16636	110.06275
community_id + day_of_week + on_time	12.04890	53.16861	110.06739
district_id + community_id + period + enum_id + day_of_week	12.04921	53.16997	110.07021
community_id + wave + day_of_week + on_time	12.04931	53.17040	110.07110
district_id + community_id + wave + period + enum_id + day_of_week	12.04962	53.17177	110.07394
district_id + community_id + day_of_week + on_time	12.05012	53.17398	110.07852
district_id + community_id + wave + day_of_week + on_time	12.05052	53.17577	110.08222
enum_id + on_time	12.05375	53.19003	110.11174
enum_id + day_of_week	12.06489	53.23915	110.21344
enum_id + day_of_week + on_time	12.06803	53.25303	110.24216
community_id + cohort + enum_id + day_of_week	12.19272	53.80326	111.38123
community_id + wave + cohort + enum_id + day_of_week	12.19314	53.80508	111.38500
district_id + community_id + cohort + enum_id + day_of_week	12.19396	53.80874	111.39257
district_id + community_id + wave + cohort + enum_id + day_of_week	12.19438	53.81056	111.39635
community_id + cohort + enum_id + day_of_week + on_time	12.19473	53.81213	111.39958
community_id + wave + cohort + enum_id + day_of_week + on_time	12.19514	53.81394	111.40334
district_id + community_id + cohort + enum_id + day_of_week + on_time	12.19597	53.81760	111.41091
district_id + community_id + wave + cohort + enum_id + day_of_week + on_time	12.19639	53.81943	111.41469
community_id + cohort + enum_id + on_time	12.20622	53.86280	111.50448
community_id + wave + cohort + enum_id + on_time	12.20663	53.86463	111.50826
district_id + community_id + cohort + enum_id + on_time	12.20746	53.86827	111.51582
district_id + community_id + wave + cohort + enum_id + on_time	12.20787	53.87010	111.51960
community_id + enum_id + day_of_week	12.24328	54.02635	111.84305
community_id + wave + enum_id + day_of_week	12.24369	54.02818	111.84684
community_id + enum_id + day_of_week + on_time	12.24395	54.02932	111.84920
community_id + wave + enum_id + day_of_week + on_time	12.24437	54.03115	111.85299
district_id + community_id + enum_id + day_of_week	12.24452	54.03184	111.85442
district_id + community_id + wave + enum_id + day_of_week	12.24494	54.03367	111.85822
district_id + community_id + enum_id + day_of_week + on_time	12.24520	54.03482	111.86059
district_id + community_id + wave + enum_id + day_of_week + on_time	12.24561	54.03665	111.86438
community_id + enum_id + on_time	12.25306	54.06951	111.93240
community_id + wave + enum_id + on_time	12.25347	54.07134	111.93619
district_id + community_id + enum_id + on_time	12.25430	54.07500	111.94377
district_id + community_id + wave + enum_id + on_time	12.25472	54.07683	111.94756

The best FE, as measured by improvement of SE as % of No FE SE, across all 4 outcomes is: district_id + wave + period + enum_id.

However, it is important to note that is only true when looking at the average. For some outcomes, even the best FE combination makes no difference (SE is ~99.36% of the SE when No FE is included). For the the next best FE combinations, they have larger SE’s for some outcomes compared to having No FE at all.

```{r}
# For each power_set_se dataset, we should merge them into a single dataset for easier comparison. Keep only the avg_se_pct_coeff, avg_se_pct_none and fe columns, adding a variable column to indicate which variable it is.
phq2_se <- phq2_power_set_se %>%
    select(fe_spec, avg_se_pct_coeff, avg_se_pct_none) %>%
    mutate(variable = "PHQ-2 Z-Score")
gad2_se <- gad2_power_set_se %>%
    select(fe_spec, avg_se_pct_coeff, avg_se_pct_none) %>%
    mutate(variable = "GAD-2 Z-Score")
consumption_se <- consumption_power_set_se %>%
    select(fe_spec, avg_se_pct_coeff, avg_se_pct_none) %>%
    mutate(variable = "Total Consumption")
income_se <- income_power_set_se %>%
    select(fe_spec, avg_se_pct_coeff, avg_se_pct_none) %>%
    mutate(variable = "Total Income")

combined_se <- bind_rows(phq2_se, gad2_se, consumption_se, income_se)


combined_se_summary <- combined_se %>%
    group_by(fe_spec) %>%
    summarise(
        mean_se_pct_coeff = mean(avg_se_pct_coeff),
        mean_se_pct_none = mean(avg_se_pct_none),
        min_se_pct_coeff = min(avg_se_pct_coeff),
        max_se_pct_coeff = max(avg_se_pct_coeff),
        min_se_pct_none = min(avg_se_pct_none),
        max_se_pct_none = max(avg_se_pct_none)
    ) %>%
    mutate(
        fe_spec = fct_reorder(fe_spec, mean_se_pct_none, .desc = TRUE)
    )
```

```{r}
#| fig.width: 10
#| fig.height: 8
p <- ggplot(combined_se_summary, aes(y = fe_spec, text = paste0(
    "FE Spec: ", fe_spec, "<br>",
    "% of No FE: ", round(mean_se_pct_none, 2), "<br>",
    "Min SE % of No FE: ", round(min_se_pct_none, 2), "<br>",
    "Max SE % of No FE: ", round(max_se_pct_none, 2)
))) + 
    # GOAL: Add no variable labels on the y-axis and instead have it show up on hover on the points(x, y = NULL, type = "p", ...)
    geom_point(aes(x = mean_se_pct_none)) +
    # Color "None" fe_spec as red
    geom_point(data = filter(combined_se_summary, fe_spec == "None"), aes(x = mean_se_pct_none), color = "red") +
    labs(
        x = "% of No FE SE (mean, min, max)",
        y = NULL
    )  + 
    theme(axis.text.y = element_blank())

ggplotly(p, tooltip = "text")
```