Epidemiology & Technology

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

Vivek GuptaAugust 8, 2020

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

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