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498 lines
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498 lines
24 KiB
Plaintext
10 months ago
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help for ^gllamm^
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Generalised linear latent and mixed models
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-------------------------------------------
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^gllamm^ depvar [varlist] [^if^ exp] [^in^ range] ^,^ ^i(^varlist^)^
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[ ^nocons^tant ^o^ffset^(^varname^)^ ^nr^f^(^#^,^...^,^#^)^
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^e^qs^(^eqnames^)^ ^frload^(^#^,^...^,^#^)^
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^ip(^string^)^ ^ni^p^(^#^,^...^,^#^)^ ^pe^qs^(^eqname^)^
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^bmat^rix^(^matrix^)^ ^ge^qs^(^eqnames^)^ ^nocor^rel
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^c^onstraints^(^clist^)^ ^we^ight^(^varname^)^ ^pwe^ight^(^varname^)^
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^f^amily^(^family^)^ ^fv(^varname^)^ ^de^nom^(^varname^)^
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^s(^eqname^)^ ^l^ink^(^link^)^ ^lv(^varname^)^
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^expa^nded^(^varname varname string^)^ ^b^asecategory^(^#^)^
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^comp^osite^(^varnames^)^ ^th^resh^(^eqnames^)^ ^eth^resh^(^eqnames^)^
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^fr^om^(^matrix^)^ ^copy^ ^skip^ ^long^
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^lf0(^#^ ^#^)^ ^ga^teaux^(^#^ ^#^ ^#^)^ ^se^arch^(^#^)^
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^noe^st ^ev^al ^in^it ^it^erate^(^#^)^ ^adoonly^ ^adapt^
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^rob^ust ^clu^ster^(^varname^)^
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^l^evel^(^#^)^ ^eform^ ^allc^ ^tr^ace ^nolo^g ^nodis^play ^do^ts
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]
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where family is and link is
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^gau^ssian ^id^entity
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^poi^sson ^log^
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^gam^ma ^rec^iprocal
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^bin^omial ^logi^t
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^pro^bit
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^cll^ (complementary log-log)
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^ll^ (log-log)
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^olo^git (o stands for ordinal)
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^opr^obit
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^ocl^l
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^mlo^git
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^spr^obit (scaled probit)
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^sop^robit
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and clist is of the form #[^-^#][^,^ #[^-^#] ...]
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^gllamm^ shares the features of all estimation commands; see help @est@.
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^gllamm^ typed without arguments redisplays previous results.
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Predictions of the latent variables or random effects (and many other
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quantities) can be obtained using @gllapred@ and the models can be
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simulated using @gllasim@
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Description
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-----------
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^gllamm^ estimates ^G^eneralized ^L^inear ^L^atent ^A^nd ^M^ixed ^M^odels.
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These models include multilevel (hierarchical) regression models
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with an arbitrary number of levels, generalized linear mixed models,
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multilevel factor models and some types of latent class models.
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We refer to the random effects (random intercepts, slopes or coefficients),
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factors, etc. as latent variables or random effects.
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If the latent variables are assumed to be multivariate normal,
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^gllamm^ uses Gauss-Hermite quadrature, or adaptive quadrature
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if the ^adapt^ option is also specified. Adaptive quadrature
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can be considerably more accurate than ordinary quadrature,
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see first reference at the bottom of this help file.
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With the ^ip(^f^)^ option, the latent variables are specified
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as discrete with freely estimated probabilities (masses) and locations.
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More information on the models is available from
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http://www.gllamm.org
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Options
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--------
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(a) Structure of the model
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---------------------------------------------------------------------------
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^i(^varlist^)^ gives the variables that define the hierarchical, nested
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clusters, from the lowest level (finest clusters) to the highest level,
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e.g. i(pupil class school).
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^noconstant^ omits the constant term from the fixed effects equation.
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^offset(^varname^)^ specifies a variable to be added to the linear predictor
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without estimating a corresponding regression coefficient (e.g. log
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exposure for Poisson regression).
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^nrf(^#^,^...^,^#^)^ specifies the number of random effects for each level,
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i.e., for each variable in ^i(^varlist^)^. The default is nrf(1,...,1).
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^eqs(^eqnames^)^ specifies equation names (defined before running gllamm)
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for the linear predictors multiplying the latent variables; see help @eq_g@.
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If required, constants should be explicitly included in the equation
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definitions using variables equal to 1. If the option is not used, the
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latent variables are assumed to be random intercepts and only one random
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effect is allowed per level. The first lambda coefficient is set to one
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unless the ^frload()^ option is specified. The other coefficients are
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estimated together with the (co)variance(s) of the random effect(s).
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^frload(^#^,^...^,^#^)^ lists the latent variables for which the first
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factor loading should be freely estimated along with the other
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factor loadings. It is up to the user to define appropriate constraints
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to identify the model. Here the latent variables are referred to
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as 1 2 3 etc. in the order in which they are defined by the ^eqs()^
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option.
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^ip(^sting^)^ if string is g, Gaussian quadrature points are used and if
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string is f, the mass-points are freely estimated. The default is
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Gaussian quadrature. The ^ip(^f^)^ option causes nip-1 locations to
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be estimated, the nipth mass being determined by setting the mean
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location to 0 so that an intercept can be included in the fixed
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effects equation. The ^ip(^fn^)^ option can be used to set the last mass
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to 0 instead of to the mean. If string is m, spherical quadrature rules
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are used for multidimensional integrals.
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^nip(^#^,^...^,^#^)^ specifies the number of integration points or masses
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to be used for each integral or summation. When quadrature is used,
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a value may be given for each random effect. When freely estimated masses
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are used, a value may be given for each level of the model. If only one
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argument is given, the same number of integration points will be used for
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each summation. Combined with the ^ip(m)^ option, ^nip()^ specifies
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the degree of the approximation instead of the number of points. Only the
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following degrees are available: for two random effects, 5, 7, 9, 11, 15
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and for more than two random effects 5, 7.
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^peqs(^eqname^)^ can be used with the ^ip(^f^)^ or ^ip(^fn^)^ options
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to allow the (prior) latent class probabilities to depend on covariates.
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The model for the latent class probabilities is a multinomial logit model
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with the last latent class as reference category. A constant is
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automatically included in addition to the covariates specified in the
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equation command; see help @eq_g@.
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^geqs(^eqnames^)^ specifies regressions of latent variables on explanatory variables.
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The second character of the equation name indicates which latent
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variable is regressed on the variables used in the equation definition, e.g.
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eq f1: a b means that the first latent variable is regressed on a and b (without
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a constant); see help @eq_g@.
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^bmatrix(^matrix^)^ specifies a matrix B of regression coefficients for the
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dependence of the latent variables on other latent variables. The matrix
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must be upper diagonal and have number of rows and columns equal to the
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total number of random effects.
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^nocorrel^ may be used to constrain all correlations to zero
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if there are several random effects at any of the levels and if these are
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modeled as multivariate normal.
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^constraint(^clist^)^ specifies the constraint numbers of the constraints to
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be applied. Constraints are defined using the ^constraint^ command; see
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help @constraint@. To find out the equation names needed to specify the
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constraints, run gllamm with the noest option.
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^weight(^varname^)^ specifies that variables varname1, varname2, etc. contain
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frequency weights. The suffixes determine at what level each weight applies.
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For example, if the level 1 units are subjects, the level 2 units are
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families, and the result is binary, we can collapse dataset A into
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dataset B as follows:
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A B
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family subject result family subject result wt1 wt2
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1 1 0 1 1 0 2 1
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1 2 0 2 3 1 1 2
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2 3 1 2 4 0 1 2
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2 4 0
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3 5 1
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3 6 0
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The level 1 weight, wt1, indicates that subject 1 in dataset B
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represents two subjects within family 1 in dataset A, whereas subjects
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3 and 4 in dataset B represent single subjects within family 2 in
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dataset A. The level 2 weight wt2 indicates that family 1 in dataset B
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represents one family and family 2 represents two families, i.e. all
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the data for family 2 are replicated once. Collapsing the data in this
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way can make gllamm run considerably faster.
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^pweight(^varname^)^ specifies that variables varname1, varname2, etc. contain
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sampling weights for levels 1, 2, etc. As far as the estimates and
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log-likelihood are concerned, the effect of specifying these
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weights is the same as for frequency weights, but the standard errors
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will be different. Robust standard errors will automatically be provided.
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This should be used with caution if the sampling weights apply
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to units at a lower level than the highest level in the multilevel model.
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The weights are not rescaled; scaling is the responsibility of the user.
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(b) Densities, links, etc. for the response model
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------------------------------------------------------------------------------
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^family(^families^)^ specifies the families to be used for the conditional
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densities. The default is ^family(^gauss^)^. Several families may be given
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in which case the variable allocating families to observations must be
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given using ^fv(^varname^)^.
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^fv(^varname^)^ is required if mixed responses requiring more than a single
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family of conditional distributions are analyzed. The variable indicates
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which family applies to which observation. A value of one refers to the
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first family etc.
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^denom(^varname^)^ gives the variable containing the binomial denominator for
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the responses whose family is specified as binomial. The default
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denominator is 1.
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^s(^eqname^)^ specifies that the log of the standard deviation (or coefficient
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of variation) at level 1 for normally (or gamma) distributed responses
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should be given by the linear predictor defined by eqname. This is
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necessary if the level-1 variance is heteroscedastic. For example, if
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dummy variables for groups are used, different variances are estimated
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for different groups.
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^link(^link^)^ specifies the links to be used for the conditional densities. If
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a single family is specified, the default link is the canonical link.
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Several links may be given in which case the variable allocating links to
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observations must be given using ^lv(^varname^)^. This option is currently
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not available if the ordinal or mlogit links are used. Numerically
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feasible choices of link depend upon the distributions of the covariates
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and choice of conditional error and random effects distributions. The
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sprobit link is only identified in special cases; it may be used for
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Heckman-type selection models or to model floor or ceiling effects.
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^lv(^varname^)^ is the variable whose values indicate which link applies to
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which observation.
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^expanded(^varname varname string^)^ is used together with the mlogit
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link and specifies that the data have been expanded as illustrated
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below:
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A B
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choice response altern selected
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1 1 1 1
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2 1 2 0
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1 3 0
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2 1 0
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2 2 1
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2 3 0
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where the variable "choice" is the multinomial response
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(possible values 1,2,3), the "response" labels the original lines
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of data, "altern" gives the possible responses or alternatives
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and "selected" is an indicator for the option that was selected.
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The syntax would be expanded(response selected m) and the variable
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"altern" would be used as the dependent variable. This expanded
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form allows the user to use different random effects etc. for
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different categories of the multinomial response. The third
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argument is o if one set of coefficients should be estimated
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for the explanatory variables and m if one set of coefficients
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is to be estimated for each category of the response except the
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reference category.
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^basecategory^(^#^)^ When the mlogit link is used, this specifies the
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value of the response to be used as the reference category. This option is
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ignored if the expanded() option is used with the third argument equal
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to m.
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^composite^(varname varname varname [more varnames]) specifies that a
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composite link is used. The first variable is a cluster identifier
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("cluster" below) so that linear predictors within the cluster can
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be combined into a single composite link. The second variable
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("ind" below) indicates to which response the composite links defined
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by the susequent weight variables belong. Observations with ind=0
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have a missing link. The remaining variables ("c1" and "c2" below)
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specify weights for the composite links. The composite link based on
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the first weight variable will go to where ind=1, etc.
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Example:
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Data setup with form of inverse link Interpretation of
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h_i determined by link() and lv(): composite(cluster ind c1 c2)
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cluster ind c1 c2 inverse link cluster composite link
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1 1 1 0 h_1 1 h_1 - h_2
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1 2 -1 1 h_2 1 n_2 + h_3
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1 0 0 1 h_3 ==> 1 missing
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2 1 1 0 h_4 2 h_4 + h_5
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2 2 1 1 h_5 2 h_5 + 2*h_6
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2 0 0 2 h_6 2 missing
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^thresh(^eqnames^)^ specifies equation(s) for the thresholds for ordinal
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response(s); see help @eq_g@. One equation is specified for each
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ordinal response. The purpose of this option is to allow the effects of some
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covariates to be different for different categories of the ordinal variable
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rather than assumming a constant effect - the proportional odds assumption
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if the ologit link is used. Variables used in the model for the
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thresholds cannot appear in the fixed part of the linear predictor.
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^ethresh(^eqnames^)^ is the same as ^thresh(^eqnames^)^ except that
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a different parameterization is used for the threshold model. To
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ensure that k_{s-1} <= k_{s}, the model is k_{s} = k_{s-1} + exp(xb),
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for response categories s=2,...,S.
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(c) Starting values
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-----------------------------------------------------------------------------
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^from(^matrix^)^ specifies the matrix to be used for the initial values.
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Note that the column-names and equation-names have to be correct
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(see help @matrname@, @matrix@), unless the ^copy^ option is specified.
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The matrix may be obtained from a previous estimation command using e(b).
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This is useful if the number of quadrature points needs to be increased
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or of a new explanatory variable is added. Use the ^skip^ option if
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the matrix of has extra parameters.
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^copy^ and ^skip^ see above.
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^long^ may be used with the from(matrix) option when constraints are used
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to indicate that the matrix of initial values has as many elements
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as would be needed for the unconstrained model, i.e. more elements
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than will be estimated.
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^lf0(^# #^)^ gives the number of parameters and the log-likelihood for a
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likelihood ratio test to compare the model to be estimated with a simpler
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model. A likelihood ratio chi-squared test is only performed if the
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^lf0(^# #^)^ option is used.
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^gateaux(^min^,^max^,^n^)^ may be used with method ip(f) to increase the
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number of mass-points by one from a previous solution with parameter
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estimates specified using from(matrix) and number of parameters and
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log-likelihood specified by lf0(# #). The program searches for the
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location of the new mass-point by placing a very small mass at the
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location given by the first argument and moving it to the second argument
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in the number of steps specified by the third argument. (If there are
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several random effects, this search is done in each dimension resulting
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in a regular grid of search points.) If the maximum increase in likelihood
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is greater than 0, the location corresponding to this maximum is used as
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the initial value of the new location, otherwise the program stops. When
|
||
|
|
this happens, it can be shown that for certain models the current solution
|
||
|
|
represents the non-parametric maximum likelihood estimate.
|
||
|
|
|
||
|
|
^search(^#^)^ causes the program to search for initial values for the random
|
||
|
|
effects at level 2 (in range 0 to 3). The argument specifies the number
|
||
|
|
of random searches. This option may only be used with ^ip(^g^)^ and when
|
||
|
|
^fr^om^(^matrix^)^ is not used.
|
||
|
|
|
||
|
|
(d) Estimation and output options
|
||
|
|
------------------------------------------------------------------------------
|
||
|
|
|
||
|
|
^noest^ is used to prevent the program from carrying out the estimation. This
|
||
|
|
may be used with the trace option to check that the model is correct and
|
||
|
|
get the information needed to set up a matrix of initial values. Global
|
||
|
|
macros are available that are normally deleted. Particularly useful may
|
||
|
|
be M_initf and M_initr, matrices for the parameters (fixed part and
|
||
|
|
random part respectively).
|
||
|
|
|
||
|
|
^eval^ causes the program to simply evaluate the loglikelihood for values passed
|
||
|
|
to it using the from(matrix) option.
|
||
|
|
|
||
|
|
^init^ causes the program to compute initial estimates of fixed effects
|
||
|
|
only, setting all latent variables to zero. gllamm will be used for
|
||
|
|
estimating initial values even if a Stata command is available for the
|
||
|
|
model (without the init option, gllamm uses Stata commands for initial values
|
||
|
|
whenever they are available).
|
||
|
|
|
||
|
|
^iterate(^#^)^ specifies the (maximum) number of iterations. With the ^adapt^
|
||
|
|
option, use of the ^iterate(^#^)^ option will cause ^gllamm^ to skip the
|
||
|
|
"Newton Raphson" iterations usually performed at the end without updating
|
||
|
|
the quadrature locations. ^iterate(^0^)^ is like ^eval^ except that standard
|
||
|
|
errors are computed.
|
||
|
|
|
||
|
|
^adoonly^ causes all gllamm to use only ado-code. Gllamm will be faster if
|
||
|
|
if it uses internalised versions of some of the functions available in
|
||
|
|
Stata 7 if updated on or after 26oct2001
|
||
|
|
|
||
|
|
^nip(^#^,^...^,^#^)^ when quadrature is used, this specifies the number
|
||
|
|
of quadrature points (integration points) to be used. A value may be
|
||
|
|
given for each random effect. If only one argument is given, the
|
||
|
|
same number of quadrature points will be used for each summation.
|
||
|
|
|
||
|
|
^adapt^ causes adaptive quadrature to be used instead of ordinary quadrature.
|
||
|
|
This option cannot be used with the ^ip(^f^)^ or ^ip(^f0^)^ options.
|
||
|
|
|
||
|
|
^robust^ specifies that the Huber/White/sandwich estimator of the covariance
|
||
|
|
matrix of the parameter estimates is to be used. If a model has been
|
||
|
|
estimated without the ^robust^ option, the robust standard errors can be
|
||
|
|
obtained by simply typing ^gllamm, robust^.
|
||
|
|
|
||
|
|
^cluster(^varname^)^ specifies that the highest level units of the GLLAMM
|
||
|
|
model are nested in even higher level clusters where ^varname^ contains
|
||
|
|
the cluster identifier. Robust standard errors will be provided that
|
||
|
|
take this clustering into account. If a model has been estimated without
|
||
|
|
this option, the robust standard errors for clustered data can be obtained
|
||
|
|
using the command ^gllamm, cluster(varname)^.
|
||
|
|
|
||
|
|
^level(^#^)^ specifies the confidence level in percent for confidence
|
||
|
|
intervals of the coefficients.
|
||
|
|
|
||
|
|
^eform^ causes the expnentiated coefficients and confidence intervals to be
|
||
|
|
displayed.
|
||
|
|
|
||
|
|
^allc^ causes all estimated parameters to be displayed in a regression table
|
||
|
|
(including the raw parameters for the random effects) in addition to the
|
||
|
|
usual output.
|
||
|
|
|
||
|
|
^trace^ causes more output to be displayed. Before estimation begins,
|
||
|
|
details of the specified model are displayed. In addition, a
|
||
|
|
detailed iteration log is shown including parameter estimates
|
||
|
|
and log-likelihood values for each iteration.
|
||
|
|
|
||
|
|
^nolog^ suppresses output for maximum likelihood iterations.
|
||
|
|
|
||
|
|
^nodisplay^ suppresses output of the estimates but still shows iteration log
|
||
|
|
unless ^nolog^ is used.
|
||
|
|
|
||
|
|
^dots^ causes a dot to be printed (if used together with trace) every time the
|
||
|
|
likelihood evaluation program is called by ml. This helps to assess how long
|
||
|
|
gllamm is likely to take to run and reassures the user that it is making
|
||
|
|
some progress when it is very slow.
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
|
||
|
|
(a) 3-level random intercept model
|
||
|
|
----------------------------------
|
||
|
|
Some response "resp" and covariate "x" are available for pupils
|
||
|
|
in different schools. "id" is the identifier or label for the pupils
|
||
|
|
and "school" is the identifier for the schools. A linear model
|
||
|
|
with random intercepts at the pupil and school levels can be specified
|
||
|
|
as follows:
|
||
|
|
|
||
|
|
. ^gllamm resp x, i(id school) adapt trace^
|
||
|
|
|
||
|
|
|
||
|
|
(b) 2-level random coefficient model - growth curve model
|
||
|
|
---------------------------------------------------------
|
||
|
|
subjects identified by "id" have been measured repeatedly over
|
||
|
|
time giving responses in "resp". "cons" is a variable equal to 1
|
||
|
|
and "time" contains the time-points. A model with a random
|
||
|
|
intercept and slope for time is specified as follows:
|
||
|
|
|
||
|
|
. ^eq int: cons^
|
||
|
|
. ^eq slope: time^
|
||
|
|
. ^gllamm resp time, i(id) nrf(2) eqs(int slope) adapt trace ^
|
||
|
|
|
||
|
|
|
||
|
|
(c) two-parameter logistic item-response model
|
||
|
|
----------------------------------------------
|
||
|
|
variable "resp" contains responses to 5 items (e.g. 5 test questions)
|
||
|
|
for each subject. The subject identifier is "id". There are five
|
||
|
|
dummy variables "i1" to "i5" for the items, e.g. "i1" is equal
|
||
|
|
to 1 if the item is item 1 and 0 otherwise.
|
||
|
|
|
||
|
|
. ^eq discrim: i1 i2 i3 i4 i5^
|
||
|
|
. ^gllamm resp i1 i2 i3 i4 i5, link(logit) fam(binom) nocons /*^
|
||
|
|
^*/ i(id) eqs(discrim) adapt trace^
|
||
|
|
|
||
|
|
|
||
|
|
Author
|
||
|
|
------
|
||
|
|
Sophia Rabe-Hesketh (sophiarh@@berkeley.edu)
|
||
|
|
as part of joint work with Andrew Pickles and Anders Skrondal.
|
||
|
|
We would like to acknowledge Colin Taylor for helping in the
|
||
|
|
early stages of gllamm development. We are also very grateful
|
||
|
|
to Stata Corporation for helping us to speed up gllamm.
|
||
|
|
|
||
|
|
Web-page
|
||
|
|
--------
|
||
|
|
http://www.gllamm.org
|
||
|
|
|
||
|
|
|
||
|
|
References (available from sophiarh@@berkeley.edu)
|
||
|
|
----------
|
||
|
|
Rabe-Hesketh, S. and Skrondal, A. (2005). Multilevel and Longitudinal
|
||
|
|
Modeling using Stata. College Station, TX: Stata Press.
|
||
|
|
|
||
|
|
Rabe-Hesketh, S., Pickles, A. and Skrondal, S. (2004).
|
||
|
|
GLLAMM Manual. U.C. Berkeley Division of Biostatistics Working
|
||
|
|
Paper Series. Working Paper 160.
|
||
|
|
see http://www.bepress.com/ucbbiostat/paper160/
|
||
|
|
|
||
|
|
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2005). Maximum
|
||
|
|
likelihood estimation of limited and discrete dependent variable
|
||
|
|
models with nested random effects. Journal of Econometrics 128, 301-323.
|
||
|
|
|
||
|
|
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2002).
|
||
|
|
Reliable estimation of generalized linear mixed models
|
||
|
|
using adaptive quadrature. The Stata Journal 2, 1-21.
|
||
|
|
|
||
|
|
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004).
|
||
|
|
Generalised multilevel structural equation modelling.
|
||
|
|
Psychometrika 69 , 167-190.
|
||
|
|
|
||
|
|
|
||
|
|
Also see
|
||
|
|
--------
|
||
|
|
|
||
|
|
Manual: ^[U] 23 Estimation and post-estimation commands^
|
||
|
|
^[U] 29 Overview of model estimation in Stata^
|
||
|
|
|
||
|
|
On-line: help for @gllapred@, @gllasim@, @ml@, @glm@, @xtreg@,
|
||
|
|
@xtlogit@, @xtpois@, @quadchk@, @test@
|