.- help for ^gllapred^ .-Predict command for gllamm ---------------------------

^gllapred^ varname [^if^ exp] [^in^ range] [,^u^ ^fac^ ^p^ ^xb^ ^ustd^ ^co^oksd ^li^npred ^mu^ ^ma^rginal ^us(^varname^)^ ^out^come^(^#^)^ ^ab^ove^(^#^,^...^,^#^)^ ^pe^arson ^d^eviance ^a^nscombe ^s^ ^ll^ ^fsample^ ^nooff^set ^adapt^ ^adoonly^ ^fr^om^(^matrix^)^ ]

where only one of ^xb^ ^u^ ^fac^ ^p^ ^li^npred ^mu^ ^pe^arson ^d^eviance ^a^nscombe ^s^ ^ll^ may be specified at a time.

Description -----------

^gllapred^ is a prediction command for @gllamm@. It computes

-- Posterior means (empirical Bayes predictions) and standard deviations of the latent variables or random effects for models estimated using gllamm (see ^u^ and ^fac^ options).

-- Posterior probabilities for two level models with discrete latent variables or random effects (see ^p^ option).

-- The fixed part of the linear predictor (^xb^ option) or the entire linear predictor (^linpred^ option) with empirical Bayes estimates substituted for the latent variables or random effects.

-- The expectation of the response (see ^mu^ option). By default, the expectation is with respect to the posterior distribution of the latent variables, but the ^marginal^ option gives the expectation with respect to the prior distribution. The ^us()^ option can be used to get the conditional expectation for specified values of the latent variables.

--- Pearson, Deviance or Anscombe residuals. By default, the posterior expectation, but the ^us^ option gives the residuals for specified values of the latent variables.

-- The level 1 standard deviation (see ^s^ option).

-- Log-likelihood contributions of the highest level clusters (see ^ll^ option).

In some cases the log-likelihood is also returned. By default prediction is restricted to the estimation sample. In this case (and if the ^if^ and ^in^ options are not specified), the log-likelihood returned by gllapred should be the same as that previously returned by gllamm.

Options --------

^u^ the posterior means and standard deviation of the latent variables or random effects are returned in "varname"m1, "varname"m2, etc., and "varname"s1, "varname"s2, etc., respectively, where the order of the latent variables is the same as in the call to gllamm (in the order of the equations in the eqs() option). In the case of continuos latent variables, the number of quadrature points used is also the same as in the previous call to gllamm. If the gllamm model includes equations for the latent variables (geqs and/or bmatrix), the posterior means and standard deviations of the disturbances are returned.

^corr^ the posterior correlations of the random effects or latent variables are returned in "varname"c21, etc. This option only works together with the ^u^ option. If the model includes equations for the latent variables, posterior correlations of the disturbances are calculated.

^fac^ If the gllamm model includes equations for the latent variables (^geqs()^ and/or ^bmatrix()^), ^fac^ causes predictions of the latent variables (e.g. factors) to be returned in "varname"m1, "varname"m2, etc. instead of the disturbances. In other words, predictions of the latent variables on the left-hand side of the equations are returned.

^p^ can only be used for two-level models estimated using the ip(f) option. gllapred returns the posterior probabilities in "varname"1, "varname"2, etc., giving the probabilities of classes 1,2, etc. gllapred also prints out the (prior) probability and location matrices to help interpret the posterior probabilities.

^xb^ the linear predictor for the fixed effects is returned. This includes the offset (if there is one in the gllamm model) unless the ^nooffset^ option is specified.

^ustd^ standardized posterior mean - approximate sampling standard deviation is used, sqrt(prior var. - posterior var.)

^cooksd^ Cook's distances for the top-level units.

^linpred^ returns the linear predictor including both the fixed and random parts where posterior means are substituted for the latent variables or random effects in the random part. The offset is included (if there is one in the gllamm model) unless the ^nooffset^ option is specified.

^mu^ returns the expecation of the response, for example the predicted probability in the case of dichotomous responses. By default, the expectation is with respect to the posterior distribution of the latent variables, but see ^marginal^ and ^us()^ options. The offset is included (if there is one in the gllamm model) unless the ^nooffset^ option is specified.

^marginal^ together with the ^mu^ option gives the expectation of the response with respect to the prior distribution of the latent variables. This is useful for looking at the 'marginal' or population average effects of covariates.

^us(^varname)^ can be used to specify values for the latent variables to calculate conditional quantities, such as the conditional mean of the responses (^mu^ option) given the values of the latent variables. Here varname specifies the stub-name (prefex) for the variables and ^gllapred^ will look for "varname"1 "varname"2, etc.

^outcome(^#^)^ specifies the outcome for which the predicted probability should be returned (^mu^ option) if there is a nominal response. This option is not necessary if the ^expanded()^ option was used in ^gllamm^ since in this case predicted probabilities are returned for all outcomes.

^above(^#^,^...^,^#^)^ specifies the events for which the predicted probabilities should be returned (^mu^ option) if there are ordinal responses. The probability of a value higher than that specified is returned for each ordinal response. A single number can be given for all ordinal responses.

^pearson^ returns Pearson residuals. By default, the posterior expectation with respect to the latent variables is returned. The ^us()^ option can be used to obtain the conditional residual when certain values are substituted for the latent variables.

^deviance^ returns deviance residuals. By default, the posterior expectation with respect to the latent variables is returned. The ^us()^ option can be used to obtain the conditional residual when certain values are substituted for the latent variables.

^anscombe^ returns Anscombe residuals. By default, the posterior expectation with respect to the latent variables is returned. The ^us()^ option can be used to obtain the conditional residual when certain values are substituted for the latent variables.

^s^ returns the scale or standard deviation. This is useful if the ^s()^ option was used in gllamm to specify level 1 heteroscedasticity.

^ll^ returns the log-likelihood contributions of the highest level (level L) units. ^adapt^ if the gllamm command did not use the adapt option, gllapred will use ordinary quadrature for computing the posterior means and standard deviations unless the adapt option is used in the gllapred command.

^fsample^ causes gllapred to return predictions for the full sample (except observations exluded due to the if and in options), not just the estimation sample. The returned log-likelihood may be missing since gllapred will not exclude observations with missing values on any of the variables used in the likelihood calculation. It is up to the user to exclude these observations using if or in.

^nooffset^ can be used together with the ^xb^, ^linpred^ or ^mu^ options to exclude the offset from the prediction. It will only make a difference if the offset option was used in gllamm.

^adoonly^ causes all gllamm to use only ado-code. This option is not necessary if gllamm was run with the adoonly option.

^from(^matrix^)^ specifies a matrix of parameters for which the predictions should be made. The column and equation names will be ignored. Without this option, the parameter estimates from the last gllamm model will be used.

Examples --------

Estimate parameters of a three level logistic regression model:

. ^gllamm resp x, i(id school) adapt trace family(binom)^

Predict random intercepts using empirical Bayes:

. ^gllapred int, u^

Predict marginal probability that resp=1 (with respect to random effects):

. ^gllapred prob, mu marginal^

Predict conditional probability that resp==1 if random intercepts are 0:

. ^gen z1 = 0^ . ^gen z2 = 0^ . ^gllapred prob, us(z)^

Predict posterior mean of Pearson residual

. ^gllapred res, pearson^

Predict Pearson residual when random effects are equal to their posterior means (note that ^gllapred int, u^ above produced empirical Bayes predictions in intm1 intm2):

. ^gllapred res, pearson us(intm)^

Author ------ Sophia Rabe-Hesketh (sophiarh@@berkeley.edu) as part of joint work with Andrew Pickles and Anders Skrondal.

Web-page -------- http://www.gllamm.org

References ---------- Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004). GLLAMM Manual. U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 160.

Also see -------- On-line: help for @gllamm@, @gllasim@