---
title: "Selecting Cases In lavaan_rerun"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Selecting Cases In lavaan_rerun}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This vignette illustrates how to select
cases when calling `lavaan_rerun()` from
the package [semfindr](https://sfcheung.github.io/semfindr/).

Instead of refitting the model *n* times, each time
with each case removed, it is possible to use some criteria
to select cases to be included in the analysis. This is useful
when the time to fit a model is long and/or the sample
size is large. This can also be used together with the
approximate approach: Use the approximate approach to
identify potentially influential case and then compute the
exact influence statistics for these cases. See
`vignette("casewise_scores", package = "semfindr")` for
further information on the the approximate approach.

The sample data set `pa_dat` will be used for illustration:

```{r}
library(semfindr)
dat <- pa_dat
# Add case id
dat <- cbind(id = paste0("case", seq_len(nrow(dat))), dat)
head(dat)
```

The following model is fitted to the data set:

```{r}
library(lavaan)
mod <-
"
iv1 ~~ iv2
m1 ~ iv1 + iv2
dv ~ m1
"
fit <- sem(mod, dat)
```

# Row Numbers or Case IDs

Suppose, for some reasons, users want to refit a model
only with selected rows removed. For example, only
rows 1, 4, 15, and 18 should be selected. This can be
done using
the argument `to_rerun` of `lavaan_rerun()`:

```{r}
rerun_out <- lavaan_rerun(fit,
                          to_rerun = c(1, 4, 15, 18))
```

Only four reruns in the output:

```{r}
rerun_out
est_change(rerun_out)
```

If user supplied case IDs are used, then the value of
`to_rerun` should be a vector of these case IDs:

```{r}
rerun_out <- lavaan_rerun(fit,
                          case_id = dat$id,
                          to_rerun = c("case1",
                                       "case4",
                                       "case15",
                                       "case18"))
```

Only four reruns in the output. User supplied case IDs
are used in the output:

```{r}
rerun_out
est_change(rerun_out)
```

# Mahalanobis Distance on Residuals

Users can select cases using their rankings on the
Mahalanobis distance computed using the regression-based
residuals. This is possible only for models with observed
variables only (i.e., path models). This is analogous to
selecting cases based on their residuals in a multiple
regression model. A path model can have more than one
endogenous variable. The residuals of a case on all
endogenous variables will be computed (as differences
between observed scores and implied scores computed
by `implied_scores()`),
and the Mahalanobis
distance will be computed using these residuals.

This is done using the argument `resid_md_top`. Users specify
the top *x* cases on this distance to be selected for
refitting a model.

```{r}
rerun_out <- lavaan_rerun(fit,
                          case_id = dat$id,
                          resid_md_top = 5)
```

Five cases were selected, as shown below:

```{r}
rerun_out
est_change(rerun_out)
```

Note that selecting cases by this method *can* miss some
influential cases. As in multiple regression, a case that
is influential on the results needs not be a case that is
poorly predicted by the exogenous variables. Therefore,
this method should be used with caution.

# Mahalanobis Distance on All Variables

Users can select cases using their rankings on the
Mahalanobis distance computed using all observed variables.
This is done using the argument `md_top`. Users specify
the top *x* cases on this distance to be selected for
refitting a model.

```{r}
rerun_out <- lavaan_rerun(fit,
                          case_id = dat$id,
                          md_top = 5)
```

Five cases were selected, as shown below:

```{r}
rerun_out
est_change(rerun_out)
```

Note that selecting cases by this method *can* miss some
influential cases (Pek & MacCallum, 2011). Unlike multiple
regression, this distance
is not a measure of leverage. For a path model, this distance
used distances from the centroid on *all* observed variables,
including exogenous variables and endogenous variables.
For a model with latent factors, this distance is affected by
both residuals and values predicted by the latent factors.
Therefore, this method should be used with caution.

# Final Remarks

If feasible, it is recommended to refit a model once for
each case, such that the influential of all cases can be
considered together. The methods above are included when
the processing time is slow and so only selected cases are
to be explored. For the final model(s),
`lavaan_rerun()` using
all cases are recommended, to serve as a final check on the
sensitivity of the results to individual cases.

# Reference

Pek, J., & MacCallum, R. (2011). Sensitivity analysis in structural equation
models: Cases and their influence. *Multivariate Behavioral Research, 46*(2),
202–228. https://doi.org/10.1080/00273171.2011.561068
