Multi-level Model in Stata – basic syntax for ‘mixed’

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

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
Code language: Stata (stata)

Two levels – repeated observations within states

use http://www.stata-press.com/data/r15/productivity

mixed gsp private emp hwy water other unemp || state:Code language: Stata (stata)

Three levels – repeated observations within states within regions

mixed gsp private emp hwy water other unemp || region: || state:Code language: Stata (stata)

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