---
title: "Comparison fits of the multiplicative structural mean model"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Comparison fits of the multiplicative structural mean model}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(OneSampleMR)
```

## Comparison fits

* Example from the **ivtools** `ivglm()` helpfile. First simulate some example data.

```{r}
set.seed(12345)
n    <- 5000
psi0 <- 0.5
psi1 <- 0.2
Z    <- rbinom(n, 1, 0.5)
X    <- rbinom(n, 1, 0.7 * Z + 0.2 * (1 - Z))
m0   <- plogis(1 + 0.8 * X - 0.39 * Z)
Y    <- rbinom(n, 1, plogis(psi0 * X + log(m0 / (1 - m0))))
dat  <- data.frame(Z, X, Y)
```

* Comparison fit using `msmm()`.

```{r}
fit02 <- msmm(Y ~ X | Z, data = dat)
summary(fit02)
```

* Comparison fit using the alternative GMM moment conditions.

```{r}
fit03 <- msmm(Y ~ X | Z, data = dat, estmethod = "gmmalt")
summary(fit03)
```

* Comparison fit using transformed variables using two-stage least squares.

```{r}
fit04 <- msmm(Y ~ X | Z, data = dat, estmethod = "tsls")
summary(fit04)
```

* Comparison fit using the alternative transformed variables approach using two-stage least squares.

```{r}
fit05 <- msmm(Y ~ X | Z, data = dat, estmethod = "tslsalt")
summary(fit05)
```