Regression and generalized linear models
GenStat provides directives for carrying out linear and nonlinear regression, also generalized
linear, generalized additive and generalized nonlinear models. They are designed to allow easy
comparison between models, and comparison between groups of data (specified as factors). The
directives for nonlinear regression can also be used for general optimization. There are three
preliminary directives for defining the form of model to be fitted, of which the MODEL
directive must always be given first:
defines the response variate(s) and the type of model to be
fitted
specifies a maximal model, containing all terms to be used in
subsequent regression models
controls iterative fitting of generalized linear models, generalized
additive models and nonlinear models, and specifies parameters and bounds for nonlinear
models
Separate directives carry out the fitting of the various types of model:
fits a linear model, a generalized linear model, a generalized additive
model, or a generalized nonlinear model
fits a standard nonlinear regression model
fits a user-defined nonlinear regression model or optimizes
a scalar function
Further directives are provided to allow sequential modification of the set of explanatory variables:
adds extra terms to any type of regression model
drops terms from any type of regression model
adds terms to, or drops them from, any type of regression
model
displays results of single-term changes to a linear or generalized
linear model
selects terms to include in or exclude from a linear or generalized
linear model
The results of fitting the models can be displayed or stored in data structures:
displays the fit of any type of regression model
stores the results from any type of regression model
forms predictions from a linear or generalized linear model
estimates functions of parameters of a regression model
Procedure relevant to regression analysis, in the regression and glm modules of the Library,
include:
checks the fit of a regression model
draws a graph to display the fit of a regression model
does random permutation and exact tests for regression or
generalized-linear-model analyses
calculates the power (probability of detection) for regression
models
calculates effective standard errors that give good approximate
sed's
displays a regression tree
constructs a regression tree
makes predictions using a regression tree
forms values for nodes of a regression tree
calculates Most Probable Numbers from dilution series data
fits models to overdispersed proportions
calculates effective doses or relative potencies
fits regression models one term at a time (useful for
obtaining an accumulated analysis of deviance table containing the contributions of individual
terms in a generalized linear model)
fits models to longitudinal data by generalized estimating
equations
analyses non-standard generalized linear models
fits a generalized linear mixed model
analyses data using a hierarchical generalized linear model
(HGLM) or a double hierarchical generalized linear model (DHGLM)
displays results from an HGLM or DHGLM
adds random terms into the dispersion models of an
HGLM, so that the whole model becomes a DHGLM
defines the fixed model for an HGLM or DHGLM
saves information from an HGLM or DHGLM analysis
produces model-checking plots for an HGLM or DHGLM
forms predictions from an HGLM or DHGLM analysis
defines the random model for an HGLM
estimates implicit and/or explicit functions of parameters
performs t-tests for pairwise differences
displays results of t-tests for pairwise differences in compact
diagrams
fits probit models allowing for natural mortality and
immunity
calculates comparison contrasts amongst regression
means
gives t-tests for all pairwise differences of means from linear or
generalized linear models
does modified joint regression analysis for variety-by-environment
data
fits a linear functional relationship model
fits a model where different units follow different generalized linear
models
fits a negative binomial GLM estimating the aggregation
parameter
fits a generalized linear model with nonnegativity
constraints (synonym FITNONNEGATIVE)
carries out analysis of parallelism for nonlinear functions
(synonym FITPARALLEL)
fits a general four-parameter growth model to a non-decreasing
response variate (synonym FITSCHNUTE)
performs screening tests for generalized or multivariate linear
models
searches through models for a regression or generalized linear
model (with methods including all-subsets, forward and backward stepwise regression)
fits two-straight-line (broken-stick) models to data
searches for the minimum of a function using the Nelder-Mead
algorithm
fits models for Wadley's problem, allowing alternative links and
errors
performs analyses of categorical data from crossover
trials
estimates the parameter lambda of a single parameter
transformation