---
title: "Economic Stress model mediation example"
vignette: >
  %\VignetteIndexEntry{estress}
  %\VignetteEngine{quarto::html}
  %\VignetteEncoding{UTF-8}
knitr:
  opts_chunk:
    collapse: true
    comment: '#>'
---

## Preamble

```{r}
#| label: setup
library(rccme)
library(modelsummary) # for model summary
```

Also install the `sandwich` package for robust standard errors, but you don't have to load it.

Summarise the dataset:

```{r}
summary(estress)
```

The goal is to fit the mediation model in Figure 4.2 of the 2017 Introduction to Process text by Andrew Hayes.

In this model, `estress`, `ese`, `sex` and `tenure` predict `affect`; and all five variables predict `withdraw`.

We already have scale average scores for `estress`, `ese`, `affect`, `withdraw`.

We also gather construct reliabilities from table 1 in the paper:

```{r}
cons_rel <- list(
  "estress" = .72, "affect" = .88, "withdraw" = .73, "ese" = .95
)
```

When using regression calibration, we need to think about each regression model, one at-a-time.

## The model for affect

In this model, `estress` and `ese` are scale predictors, i.e., measured with error. `sex` and `tenure` are assumed to be measured without error.

Prior to regression, we calibrate the `estress` and `ese` scores. We pass the covariates measured without error using the `z_mat` argument.

```{r}
cal_for_aff_out <- rccme_calib_me(
  estress[, c("estress", "ese")],
  rel_vec = c(cons_rel$estress, cons_rel$ese),
  z_mat = estress[, c("sex", "tenure")]
)
head(cal_for_aff_out)
estress$estress_to_aff <- cal_for_aff_out[, "estress"]
estress$ese_to_aff <- cal_for_aff_out[, "ese"]
```

Now we can run the regression:

```{r}
(fit_aff_cal <- lm(
  affect ~ estress_to_aff + ese_to_aff + sex + tenure, estress
))
```

We also run the regression with the original variables:

```{r}
(fit_aff_no_cal <- lm(
  affect ~ estress + ese + sex + tenure, estress
))
```

We see the estress coefficient is larger with the calibrated variable.

## The model for withdraw

In this model, `estress`, `ese` and `affect` are scale predictors, i.e., measured with error. `sex` and `tenure` are assumed to be measured without error.

Prior to regression, we calibrate the `estress`, `ese` and `affect` scores:

```{r}
cal_for_wth_out <- rccme_calib_me(
  estress[, c("estress", "ese", "affect")],
  rel_vec = c(cons_rel$estress, cons_rel$ese, cons_rel$affect),
  z_mat = estress[, c("sex", "tenure")]
)
head(cal_for_wth_out)
estress$estress_to_wth <- cal_for_wth_out[, "estress"]
estress$ese_to_wth <- cal_for_wth_out[, "ese"]
estress$affect_to_wth <- cal_for_wth_out[, "affect"]
```

Now we can run the regression:

```{r}
(fit_wth_cal <- lm(
  withdraw ~ estress_to_wth + ese_to_wth + affect_to_wth + sex + tenure,
  estress
))
```

We also run the regression with the original variables:

```{r}
(fit_wth_no_cal <- lm(
  withdraw ~ estress + ese + affect + sex + tenure, estress
))
```

We see the estress and affect coefficients are larger with the calibrated variables.

## Summarise all models

```{r}
modelsummary(
  list(
    "Affect (No Calibration)" = fit_aff_no_cal,
    "Affect (With Calibration)" = fit_aff_cal,
    "Withdraw (No Calibration)" = fit_wth_no_cal,
    "Withdraw (With Calibration)" = fit_wth_cal
  ),
  estimate = "{estimate} ({std.error})", statistic = "{p.value}",
  # Set standard error to HCSEs and omit distracting fit indices
  gof_omit = "IC|F|Log", vcov = "HC4",
  # Rename calibrated variables:
  coef_rename = c(
    "estress_to_aff" = "estress", "estress_to_wth" = "estress",
    "ese_to_aff" = "ese", "ese_to_wth" = "ese", "affect_to_wth" = "affect"
  )
)
```

## Original paper for dataset

Pollack, J. M., VanEpps, E. M., & Hayes, A. F. (2012). The moderating role of social ties on entrepreneurs’ depressed affect and withdrawal intentions in response to economic stress. _Journal of Organizational Behavior, 33_(6), 789–810. https://doi.org/10.1002/JOB.1794