Stata 15 help for meglm postestimation

[ME] meglm postestimation -- Postestimation tools for meglm

Postestimation commands

The following postestimation command is of special interest after meglm:

Command Description ------------------------------------------------------------------------- estat group summarize the composition of the nested groups estat icc estimate intraclass correlations estat sd display variance components as standard deviations and correlations -------------------------------------------------------------------------

The following standard postestimation commands are also available:

Command Description ------------------------------------------------------------------------- contrast contrasts and ANOVA-style joint tests of estimates estat ic Akaike's and Schwarz's Bayesian information criteria (AIC and BIC) estat summarize summary statistics for the estimation sample estat vce variance-covariance matrix of the estimators (VCE) estat (svy) postestimation statistics for survey data estimates cataloging estimation results * hausman Hausman's specification test lincom point estimates, standard errors, testing, and inference for linear combinations of coefficients * lrtest likelihood-ratio test margins marginal means, predictive margins, marginal effects, and average marginal effects marginsplot graph the results from margins (profile plots, interaction plots, etc.) nlcom point estimates, standard errors, testing, and inference for nonlinear combinations of coefficients predict predictions, residuals, influence statistics, and other diagnostic measures predictnl point estimates, standard errors, testing, and inference for generalized predictions pwcompare pairwise comparisons of estimates test Wald tests of simple and composite linear hypotheses testnl Wald tests of nonlinear hypotheses ------------------------------------------------------------------------- * hausman and lrtest are not appropriate with svy estimation results.

Syntax for predict

Syntax for obtaining predictions of the outcome and other statistics

predict [type] newvarsspec [if] [in] [, statistic options]

Syntax for obtaining estimated random effects and their standard errors

predict [type] newvarsspec [if] [in], reffects [re_options]

Syntax for obtaining ML scores

predict [type] newvarsspec [if] [in], scores

newvarsspec is stub* or newvarlist.

statistic Description ------------------------------------------------------------------------- Main mu mean response; the default pr synonym for mu for ordinal and binary response models eta fitted linear predictor xb linear predictor for the fixed portion of the model only stdp standard error of the fixed-portion linear prediction density predicted density function distribution predicted distribution function residuals raw residuals; available only with the Gaussian family pearson Pearson residuals deviance deviance residuals anscombe Anscombe residuals ------------------------------------------------------------------------- These statistics are available both in and out of sample; type predict ... if e(sample) ... if wanted only for the estimation sample.

options Description ------------------------------------------------------------------------- Main conditional(ctype) compute statistic conditional on estimated random effects; default is conditional(ebmeans) marginal compute statistic marginally with respect to the random effects nooffset make calculation ignoring offset or exposure outcome(outcome) outcome category for predicted probabilities for ordinal models

Integration int_options integration options ------------------------------------------------------------------------- pearson, deviance, anscombe may not be combined with marginal. For ordinal outcomes, you can specify one or k new variables in newvarlist with mu and pr, where k is the number of outcomes. If you do not specify outcome(), these options assume outcome(#1).

ctype Description ------------------------------------------------------------------------- ebmeans empirical Bayes means of random effects; the default ebmodes empirical Bayes modes of random effects fixedonly prediction for the fixed portion of the model only -------------------------------------------------------------------------

re_options Description ------------------------------------------------------------------------- Main ebmeans use empirical Bayes means of random effects; the default ebmodes use empirical Bayes modes of random effects reses(stub*|newvarlist) calculate standard errors of empirical Bayes estimates

Integration int_options integration options -------------------------------------------------------------------------

int_options Description ------------------------------------------------------------------------- intpoints(#) use # quadrature points to compute marginal predictions and empirical Bayes means iterate(#) set maximum number of iterations in computing statistics involving empirical Bayes estimators tolerance(#) set convergence tolerance for computing statistics involving empirical Bayes estimators -------------------------------------------------------------------------

Menu for predict

Statistics > Postestimation

Description for predict

predict creates a new variable containing predictions such as mean responses; linear predictions; density and distribution functions; standard errors; and raw, Pearson, deviance, and Anscombe residuals.

Options for predict

+------+ ----+ Main +-------------------------------------------------------------

mu, the default, calculates the expected value of the outcome.

pr calculates predicted probabilities and is a synonym for mu. This option is available only for ordinal and binary response models.

eta calculates the fitted linear prediction.

xb calculates the linear prediction xb using the estimated fixed effects (coefficients) in the model. This is equivalent to fixing all random effects in the model to their theoretical (prior) mean value of 0.

stdp calculates the standard error of the fixed-effects linear predictor xb.

density calculates the density function. This prediction is computed using the current values of the observed variables, including the dependent variable.

distribution calculates the distribution function. This prediction is computed using the current values of the observed variables, including the dependent variable.

residuals calculates raw residuals, that is, responses minus the fitted values. This option is available only for the Gaussian family.

pearson calculates Pearson residuals. Pearson residuals that are large in absolute value may indicate a lack of fit.

deviance calculates deviance residuals. Deviance residuals are recommended by McCullagh and Nelder (1989) as having the best properties for examining the goodness of fit of a GLM. They are approximately normally distributed if the model is correctly specified. They can be plotted against the fitted values or against a covariate to inspect the model fit.

anscombe calculates Anscombe residuals, which are designed to closely follow a normal distribution.

conditional(ctype) and marginal specify how random effects are handled in computing statistic.

conditional() specifies that statistic will be computed conditional on specified or estimated random effects.

conditional(ebmeans), the default, specifies that empirical Bayes means be used as the estimates of the random effects. These estimates are also known as posterior mean estimates of the random effects.

conditional(ebmodes) specifies that empirical Bayes modes be used as the estimates of the random effects. These estimates are also known as posterior mode estimates of the random effects.

conditional(fixedonly) specifies that all random effects be set to zero, equivalent to using only the fixed portion of the model.

marginal specifies that the predicted statistic be computed marginally with respect to the random effects, which means that statistic is calculated by integrating the prediction function with respect to all the random effects over their entire support.

Although this is not the default, marginal predictions are often very useful in applied analysis. They produce what are commonly called population-averaged estimates. They are also required by margins.

nooffset is relevant only if you specified offset(varname_o) or exposure(varname_e) with meglm. It modifies the calculations made by predict so that they ignore the offset or the exposure variable; the linear prediction is treated as xb rather than xb + offset or xb + exposure, whichever is relevant.

outcome(outcome) specifies the outcome for which the predicted probabilities are to be calculated. outcome() should contain either one value of the dependent variable or one of #1, #2, ..., with #1 meaning the first category of the dependent variable, #2 meaning the second category, etc.

reffects calculates estimates of the random effects using empirical Bayes predictions. By default, or if the ebmeans option is specified, empirical Bayes means are computed. With the ebmodes option, empirical Bayes modes are computed. You must specify q new variables, where q is the number of random-effects terms in the model. However, it is much easier to just specify stub* and let Stata name the variables stub1, stub2,...,stubq for you.

ebmeans specifies that empirical Bayes means be used as the estimates of the random effects.

ebmodes specifies that empirical Bayes modes be used as the estimates of the random effects.

reses(stub*|newvarlist) calculates standard errors of the empirical Bayes estimators and stores the result in newvarlist. This option requires the reffects option. You must specify q new variables, where q is the number of random-effects terms in the model. However, it is much easier to just specify stub* and let Stata name the variables stub1, stub2,...,stubq for you. The new variables will have the same storage type as the corresponding random-effects variables.

The reffects and reses() options often generate multiple new variables at once. When this occurs, the random effects (and standard errors) contained in the generated variables correspond to the order in which the variance components are listed in the output of meglm. The generated variables are also labeled to identify their associated random effect.

scores calculates the scores for each coefficient in e(b). This option requires a new variable list of length equal to the number of columns in e(b). Otherwise, use the stub* syntax to have predict generate enumerated variables with prefix stub.

+-------------+ ----+ Integration +------------------------------------------------------

intpoints(#) specifies the number of quadrature points used to compute marginal predictions and the empirical Bayes means; the default is the value from estimation.

iterate(#) specifies the maximum number of iterations when computing statistics involving empirical Bayes estimators; the default is the value from estimation.

tolerance(#) specifies convergence tolerance when computing statistics involving empirical Bayes estimators; the default is the value from estimation.

Syntax for margins

margins [marginlist] [, options]

margins [marginlist] , predict(statistic ...) [predict(statistic ...) ...] [options]

statistic Description ------------------------------------------------------------------------- mu mean response; the default pr synonym for mu for ordinal and binary response models eta fitted linear predictor xb linear predictor for the fixed portion of the model only stdp not allowed with margins density not allowed with margins distribution not allowed with margins residuals not allowed with margins pearson not allowed with margins deviance not allowed with margins anscombe not allowed with margins reffects not allowed with margins scores not allowed with margins ------------------------------------------------------------------------- Options conditional(ebmeans) and conditional(ebmodes) are not allowed with margins. Option marginal is assumed where applicable if conditional(fixedonly) is not specified.

Statistics not allowed with margins are functions of stochastic quantities other than e(b).

For the full syntax, see [R] margins.

Menu for margins

Statistics > Postestimation

Description for margins

margins estimates margins of response for mean responses and linear predictions.

Examples

--------------------------------------------------------------------------- Setup . webuse towerlondon . meglm dtlm difficulty i.group || family: || subject:, family(bernoulli)

Obtain predicted probabilities based on the contribution of both fixed effects and random effects . predict pr

Obtain predicted probabilities based on the contribution of fixed effects only . predict prfixed, conditional(fixedonly)

Obtain predictions of the posterior means and their standard errors . predict re_means*, reses(se_means*) reffects

Obtain predictions of the posterior modes and their standard errors . predict re_modes*, reses(se_modes*) reffects ebmodes

--------------------------------------------------------------------------- Setup . use http://www.stata-press.com/data/mlmus3/schiz, clear . generate impso = imps . recode impso -9=. 1/2.4=1 2.5/4.4=2 4.5/5.4=3 5.5/7=4 . meglm impso week treatment || id:, family(ordinal)

Obtain predicted probabilities for each outcome based on the contribution of both fixed effects and random effects . predict pr*

--------------------------------------------------------------------------- Setup . use http://www.stata-press.com/data/mlmus3/drvisits, clear . meglm numvisit reform age married loginc || id: reform, family(poisson)

Obtain the predicted counts based on the contribution of both fixed effects and random effects . predict n

---------------------------------------------------------------------------

Reference

McCullagh, P., and J. A. Nelder. 1989. Generalized Linear Models. 2nd ed. London: Chapman & Hall/CRC.


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