Commands used – xtmixed (older versions, aslo used in Sophia Rabe-hesketh book) or mixed (Stata 15 and newer).

By default, xtmixed includes a random intercept

## Model Specification

- Outcome variable
**Fixed Effects part of the model-**- double pipe – ||
**Random part of the model**- Cluster identfier – example subject id within whom the observations are repeated (correlated residuals are expected within the same subject) – the random Intercept
- Colon
- Random slope variables
- comma, random effect options

**Random Effect Options**– Specifed immediately after the RE variables- covariance(vartype) variance-covariance structure of the random effects
- independent
- exchangeable
- identity
- unstructured

- noconstant – suppress constant term from the random-effects equation
- collinear – keep collinear variables

- covariance(vartype) variance-covariance structure of the random effects

## Model Options

- Fit Model via maximal likelyghood estimation – mle
- Fit model via restricted maximum likelihood (REML) – reml
- To omit random intercept – noconstant
- Specify Structure of residual errors of lowest level of observation – residual(rspec) – independent, exchangeable, autoregressive ar #, moving-average ma #, unstructured banded #, toeplitz #, or exponential

## Example

```
# Random Intercept without covariates
xtmixed wm || id:, mle
# Random Intercept with covariates
xtmixed gcse lrt || school:, mle
# Random Intercept with covariates and Random-coefficient / random slope
xtmixed gcse lrt || school: lrt, covariance(unstructured) mle
xtmixed gcse lrt || school: lrt, covariance(unstructured) mle variance // to report variances
xtmixed lwage black hisp union married exper yeart ///
educt || nr: exper, covariance(unstructured) mle
```

## Two levels – repeated observations within states

```
use http://www.stata-press.com/data/r15/productivity
mixed gsp private emp hwy water other unemp || state:
```

## Three levels – repeated observations within states within regions

`mixed gsp private emp hwy water other unemp || region: || state:`

Note that the left most part of equation are the observations (LOWERMOST LEVEL), Then is the TOP level. Finally the intermediate level. : **state nested within regions**

*There is no straight line order !* This example is straight from the STATA manual for **mixed**