Title stata.com mixed — Multilevel mixed-effects linear ...

1 Multilevel mixed -effects linear regressionDescriptionQuick startMenuSyntaxOptionsRemarks and examplesStored resultsMethods and formulasAcknowledgmentsReferencesAlso seeDescriptionmixedfits linear mixed -effects models. These models are also known as Multilevel models orhierarchical linear models. The overall error distribution of the linear mixed -effects model is assumed tobe Gaussian, and heteroskedasticity and correlations within lowest-level groups also may be startLinear mixed -effects model ofyonxwith random intercepts bylev2mixed y x || lev2:As above, but perform restricted maximum-likelihood (REML) estimation instead of the defaultmaximum likelihood (ML) estimationmixed y x || lev2.

2 , remlAs above, but perform small-sample inference onxusing the Kenward Roger degrees of freedom(DF) methodmixed y x || lev2:, reml dfmethod(kroger)Add random coefficients onxmixed y x || lev2: xAs above, but allow correlation between the random slopes and interceptsmixed y x || lev2: x, covariance(unstructured)Three-level model with random intercepts bylev2andlev3forlev2nested withinlev3mixed y x || lev3: || lev2:Crossed-effects model with two-way crossed effects by factorsaandbmixed y x || _ || b:MenuStatistics> Multilevel mixed -effects models> linear regression12 mixed Multilevel mixed -effects linear regressionSyntaxmixeddepvar feequation[||reequation] [|| ] [,options]where the syntax offeequationis[indepvars] [if] [in] [weight] [,feoptions]and the syntax ofreequationis one of the following:for random coefficients and interceptslevelvar:[varlist] [,reoptions]for random effects among the values of a factor variable in a crossed-effects modellevelvar.

3 [,reoptions]levelvaris a variable identifying the group structure for the random effects at that level or isallrepresenting one group comprising all constant term from the fixed-effects equationconstraints(constraints)apply specified linear constraintsreoptionsDescriptionModelcova riance(vartype)variance covariance structure of the random effectsnoconstantsuppress constant term from the random-effects equationfweight(exp)frequency weights at higher levelspweight(exp)sampling weights at higher levelscollinearkeep collinear variablesmixed Multilevel mixed -effects linear regression 3optionsDescriptionModelmlefit model via maximum likelihood; the defaultremlfit model via restricted maximum likelihooddfmethod(dfmethod)specify method for computingDFof atdistributionresiduals(restype[,resopts ])structure of residual errorspwscale(scalemethod)control scaling of sampling weights in two-level modelsSE/Robustvce(vcetype)vcetypemay beoim,robust, orclusterclustvar.

4 Types otherthanoimmay not be combined withdfmethod()Reportinglevel(#)set confidence level; default islevel(95)varianceshow random-effects and residual-error parameter estimates asvariances and covariances; the defaultstddeviationsshow random-effects and residual-error parameter estimates asstandard deviations and correlationsdftable(dftable)specify contents of fixed-effects table; requiresdfmethod()atestimationnoretables uppress random-effects tablenofetablesuppress fixed-effects tableestmetricshow parameter estimates as stored ine(b)noheadersuppress output headernogroupsuppress table summarizing groupsnostderrdo not estimate standard errors of random-effects parametersnocnsreportdo not display constraintsdisplayoptionscontrol columns and column formats, row spacing, line width,display of omitted variables and base and empty cells, andfactor-variable labelingEM optionsemiterate(#)number ofEMiterations.

5 Default isemiterate(20)emtolerance(#)EMconvergen ce tolerance; default isemtolerance(1e-10)emonlyfit model exclusively usingEMemlogshowEMiteration logemdotsshowEMiterations as dotsMaximizationmaximizeoptionscontrol the maximization process; seldom usedmatsqrtparameterize variance components using matrix square roots;the defaultmatlogparameterize variance components using matrix logarithmssmallreplay small-sample inference resultscoeflegenddisplay legend instead of statistics4 mixed Multilevel mixed -effects linear regressionvartypeDescriptionindependento ne unique variance parameter per random effect, all covariances 0;the default unless is usedexchangeableequal variances for random effects, and one common pairwisecovarianceidentityequal variances for random effects, all covariances 0.

6 The default if is usedunstructuredall variances and covariances to be distinctly estimateddfmethodDescriptionresidualresi dual degrees of freedom,n rank(X)repeatedrepeated-measuresANOVA anovaANOVA satterthwaite[,dfopts]generalized Satterthwaite approximation;REML estimation onlykroger[,dfopts]Kenward Roger;REML estimation Gaussian within-group errors with one common variance;the defaultexchangeablewithin-group errors with equal variances and one commoncovariancear[#]within-group errors with autoregressive (AR) structure of order#,AR(#);ar 1is implied byarma[#]within-group errors with moving-average (MA) structure of order#,MA(#);ma 1is implied bymaunstructuredwithin-group errors with distinct variances and covariancesbanded[#]within-group errors with distinct variances and covariances withinfirst#off-diagonals.

7 Bandedimplies all matrix bands(unstructured)toeplitz[#]within-gro up errors have Toeplitz structure of order#;toeplitzimplies that all matrix off-diagonals be estimatedexponentialwithin-group errors with an exponential function for the pairwisecorrelations and one overall error variancescalemethodDescriptionsizescale first-level (observation-level) weights to sum to the sample sizeof their corresponding second-level clustereffectivescale first-level weights to sum to the effective sample size of theircorresponding second-level clustergkset second-level weights to the cluster averages of the products ofthe weights at both levels and first-level weights to 1mixed Multilevel mixed -effects linear regression 5dftableDescriptiondefaulttest statistics,p-values, and confidence intervals.

8 The defaultciDFs and confidence intervalspvalueDFs, test statistics, andp-valuesindepvarsandvarlistmay contain factor variables; see[U] Factor ,indepvars, andvarlistmay contain time-series operators; see[U] Time-series ,bootstrap,by,collect,jackknife,mi estimate,rolling, andstatsbyare allowed; see[U] Prefixcommands. For more details, see [BAYES]bayes: estimateis not allowed ifdfmethod()is are not allowed with thebootstrapprefix; see [R] andfweights are allowed; see[U] weight. However, no weights are allowed if either optionremlor optiondfmethod()is not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation Model noconstantsuppresses the constant (intercept) term and may be specified for the fixed-effectsequation and for any of or all the random-effects (vartype)specifies the structure of the covariance matrix for the random effects andmay be specified for each random-effects one of the following.

9 Independent,exchangeable,identity, for a distinct variance for each random effect within a random-effects equationand assumes that all covariances are one common variance for all random effects and one common short for multiple of the identity ; that is, all variances are equal and all covariancesare for all variances and covariances to be distinct. If an equation consistsofprandom-effects terms, the unstructured covariance matrix will havep(p+1)/2 (independent)is the default, except when is used, in whichcasecovariance(identity)is the default and onlycovariance(identity)andcovari-ance(e xchangeable)are (exp)specifies frequency weights at higher levels in a Multilevel model, whereas frequencyweights at the first level (the observation level) are specified in the usual manner, for example,[fw=fwtvar1].

10 Expcan be any valid Stata variable, and you can specifyfweight()at level