Supported Models
We list here all models implemented in Zelig, organized by the nature
of the dependent variable(s) to be predicted, explained, or described.
- Continuous Unbounded dependent variables can take any
real value in the range
11#11
. While most of these
models take a continuous dependent variable, Bayesian factor analysis takes multiple
continuous dependent variables.
- "ls": The linear least-squares (see Section )
calculates the coefficients that minimize the sum of squared
residuals. This is the usual method of computing linear
regression coefficients, and returns unbiased estimates of
12#12
and 13#13
(conditional on the specified model).
- "normal": The Normal (see Section ) model
computes the maximum-likelihood estimator for a Normal
stochastic component and linear systematic component. The
coefficients are identical to ls, but the
maximum likelihood estimator for 13#13
is consistent
but biased.
- "normal.bayes": The Bayesian Normal regression
model (Section ) is similar to maximum likelihood Gaussian
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- "netls": The network least squares
regression (Section ) is similar to least squares regression
for continuous-valued proximity matrix dependent variables. Proximity
matrices are also known as sociomatrices, adjacency matrices, and
matrix representations of directed graphs.
- "tobit": The tobit regression model (see
Section ) is a Normal distribution with left-censored observations.
- "tobit.bayes": The Bayesian tobit distribution
(see Section ) is a Normal distribution that has either
left and/or right censored observations.
- "arima": Use auto-regressive, integrated, moving-average
(ARIMA) models for time series data (see Section .
- "factor.bayes": The Bayesian factor analysis model (see
Section ) estimates multiple observed continuous dependent variables
as a function of latent explanatory variables.
- Dichotomous dependent variables consist of two discrete
values, usually 14#14
.
- "logit": Logistic regression (see Section )
specifies 15#15
to be a(n inverse) logistic transformation
of a linear function of a set of explanatory variables.
- "relogit": The rare events logistic regression
option (see Section ) estimates the same model as the
logit, but corrects for bias due to rare events (when one of the
outcomes is much more prevalent than the other). It also
optionally uses prior correction to correct for choice-based
(case-control) sampling designs.
- "logit.bayes": Bayesian logistic regression (see
Section ) is similar to maximum likelihood logistic
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- "probit": Probit regression (see Section )
Specifies 15#15
to be a(n inverse) CDF normal transformation
as a linear function of a set of explanatory variables.
- "probit.bayes": Bayesian probit regression (see
Section ) is similar to maximum likelihood probit
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- "netlogit": The network logistic
regression (Section ) is similar to logistic regression
for binary-valued proximity matrix dependent variables. Proximity
matrices are also known as sociomatrices, adjacency matrices, and
matrix representations of directed graphs.
- "blogit": The bivariate logistic model (see
Section ) models
16#16
for
17#17
according
to a bivariate logistic density.
- "bprobit": The bivariate probit model (see
Section ) models
16#16
for
17#17
according to a bivariate normal density.
- "irt1d": The one-dimensional item response model
(see Section ) takes multiple dichotomous dependent variables and models
them as a function of one latent (unobserved) explanatory variable.
- "irtkd": The k-dimensional item response model
(see Section ) takes multiple dichotomous dependent variables and models
them as a function of 3#3
latent (unobserved) explanatory variables.
- Ordinal are used to model
ordered, discrete dependent variables. The values of the outcome
variables (such as kill, punch, tap, bump) are ordered, but the
distance between any two successive categories is not known
exactly. Each dependent variable may be thought of as linear, with
one continuous, unobserved dependent variable observed through a mechanism
that only returns the ordinal choice.
- "ologit": The ordinal logistic model (see
Section ) specifies the stochastic component of the
unobserved variable to be a standard logistic distribution.
- "oprobit": The ordinal probit distribution (see
Section ) specifies the stochastic component of the
unobserved variable to be standardized normal.
- "oprobit.bayes": Bayesian ordinal probit model
(see Section ) is similar to ordinal probit
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- "factor.ord": Bayesian ordered factor analysis
(see Section ) models observed, ordinal dependent variables
as a function of latent explanatory variables.
- Multinomial dependent variables are unordered, discrete
categorical responses. For example, you could model an
individual's choice among brands of orange juice or among
candidates in an election.
- "mlogit": The multinomial logistic model (see
Section ) specifies categorical responses distributed
according to the multinomial stochastic component and logistic
systematic component.
- "mlogit.bayes": Bayesian multinomial logistic regression (see
Section ) is similar to maximum likelihood multinomial logistic
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- Count dependent variables are non-negative integer
values, such as the number of presidential vetoes or the number of
photons that hit a detector.
- "poisson": The Poisson model (see
Section ) specifies the expected number of events that
occur in a given observation period to be an exponential
function of the explanatory variables. The Poisson stochastic
component has the property that,
18#18
.
- "poisson.bayes": Bayesian Poisson regression (see
Section ) is similar to maximum likelihood Poisson
regression, but makes valid small sample inferences via draws from the
exact posterior and also allows for priors.
- "negbin": The negative binomial model (see
Section ) has the same systematic component as the Poisson,
but allows event counts to be over-dispersed, such that
19#19
.
- Continuous Bounded dependent variables
that are continuous only over a certain range, usually
20#20
.
In addition, some models (exponential, lognormal, and
Weibull) are also censored for values greater than some censoring
point, such that the dependent variable has some units fully observed
and others that are only partially observed (censored).
- "gamma": The Gamma model (see Section ) for
positively-valued, continuous dependent variables that are fully
observed (no censoring).
- "exp": The exponential model (see Section ) for
right-censored dependent variables assumes that the hazard function
is constant over time. For some variables, this may be an unrealistic
assumption as subjects are more or less likely to fail the longer
they have been exposed to the explanatory variables.
- "weibull": The Weibull model (see Section )
for right-censored dependent variables relaxes the
assumption of constant hazard by including an additional scale
parameter 21#21
: If
22#22
, the risk of failure increases
the longer the subject has survived; if
23#23
, the risk of
failure decreases the longer the subject has survived. While zelig() estimates 21#21
by default, you may optionally fix
21#21
at any value greater than 0. Fixing
24#24
results
in an exponential model.
- "lognorm": The log-normal model (see
Section ) for right-censored duration dependent variables
specifies the hazard function non-monotonically, with increasing
hazard over part of the observation period and decreasing hazard
over another.
- Mixed dependent variables include models that take more
than one dependent variable, where the dependent variables come from
two or more of categories above. (They do not need
to be of a homogeneous type.)
- The Bayesian mixed factor analysis model, in contrast to the Bayesian factor
analysis model and ordinal factor analysis model, can model both types
of dependent variables as a function of latent explanatory variables.
- Ecological inference models estimate unobserved internal
cell values given contingency tables with observed row and column
marginals.
- ei.hier: The hierarchical EI model
(see Section ) produces estimates for a cross-section of
25#25
tables.
- ei.dynamic: Quinn's dynamic Bayesian EI model (see
Section ) estimates a dynamic Bayesian model for
25#25
tables with temporal dependence across tables.
- ei.RxC: The
26#26
EI model (see Section )
estimates a hierarchical Multinomial-Dirichlet EI model for
contingency tables with more than 2 rows or columns.
Gary King
2011-11-29