# Technical Details: Different Output between Stata and ggeffects

#### Daniel Lüdecke

#### 2024-02-27

Source:`vignettes/technical_stata.Rmd`

`technical_stata.Rmd`

## Why is the output from Stata different from the output from ggeffect?

Stata’s equivalent to the adjusted predictions produced by
*ggeffects* is the `margins`

-command. However, the
results are not always identical. For models from non-gaussian families,
point estimates for the adjusted predictions are identical, but the
confidence intervals differ.

Here is an explanation, why there is a difference. First, we fit a logistic regression model.

```
library(magrittr)
set.seed(5)
data <- data.frame(
outcome = rbinom(100, 1, 0.5),
var1 = rbinom(100, 1, 0.1),
var2 = rnorm(100, 10, 7)
)
m <- glm(
outcome ~ var1 * var2,
data = data,
family = binomial(link = "logit")
)
```

### Example with graphical output

#### The Stata plot

This is the code in Stata to produce an adjusted predictions plot.

```
use data.dta, clear
quietly logit outcome c.var1##c.var2
quietly margins, at(var2 = (-8(0.5)28) var1 = (0 1))
marginsplot
```

The resulting image looks like this.

#### The ggeffects plot

When we use *ggeffects*, the plot slighlty differs.

As we can see, the confidence intervals in the Stata plot are outside
the plausible range of `[0, 1]`

, which means that the
predicted uncertainty from the Stata output has a probability higher
than 1 and lower than 0, while `predict_response()`

computes
confidence intervals *within* the possible range.

### Conclusion

It seems like Stata returns incorrect confidence intervals.
Predictions and standard errors returned in Stata are on the
(transformed) response scale. Obviously, the confidence intervals are
then computed by `estimate +/- 1.96 * standard error`

, which
may lead to confidence intervals that are out of reasonable bounds
(e.g. above 1 or below 0 for predicted probabilities).

The *transformed estimate* (on the response scale) is always
between 0 and 1, and the same is true for the *transformed standard
errors*. However, adding or subtracting approx. 2 *
*transformed* SE to the *transformed* estimate does no
longer ensure that the confidence intervals are within the correct
range.

The precise way to do the calculation is to calculate estimates, standard errors and confidence intervals on the (untransformed) scale of the linear predictor and then back-transform.