---
title: "MAR1 State-Space Model"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{MAR1-State-Space}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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

```{r setup}
library(MAR1)
library(MARSS)
```

**These examples take 1-2 minutes to run**

## Construct a MAR model

We will use [run.mar()] arguments to set variables and restrictions. See the [run.mar()] page for information. No restrictions on the restriction matrix (all 0.5).

```{r}
data(L4.mar)
myvar <- c(0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2) # 8 variates, 3 covariates
myres <- matrix(0.5,
  nrow = length(which(myvar == 1)),
  ncol = length(which(myvar != 0))
)
```

Fit a MAR1 model first.

```{r}
run1 <- run.mar(L4.mar, variables = myvar, restrictions = myres, search = "exhaustive")
```

## Fit state-space model

This allows use to include observation error. `control` can be passed in to limit the number of iterations run.

```{r}
ss.fit <- ss.mar1(L4.mar, run1, control = list(maxit = 50))
```

## Compare to best fit model

```{r}
ss.fit$B
run1$bestfit$B
```

## Use a known observation error

```{r}
R <- diag(0.2, 8)
ss.fit <- ss.mar1(L4.mar, run1, model = list(R = R), control = list(maxit = 50))
```