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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:

    MODEL defines the response variate(s) and the type of model to be fitted
    TERMS specifies a maximal model, containing all terms to be used in subsequent regression models
    RCYCLE 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:

    FIT fits a linear model, a generalized linear model, a generalized additive model, or a generalized nonlinear model
    FITCURVE fits a standard nonlinear regression model
    FITNONLINEAR 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:

    ADD adds extra terms to any type of regression model
    DROP drops terms from any type of regression model
    SWITCH adds terms to, or drops them from, any type of regression model
    TRY displays results of single-term changes to a linear or generalized linear model
    STEP 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:

    RDISPLAY displays the fit of any type of regression model
    RKEEP stores the results from any type of regression model
    RKESTIMATES saves estimates and other information about individual terms in a regression analysis
    PREDICT forms predictions from a linear or generalized linear model
    RFUNCTION estimates functions of parameters of a regression model
    RSPREADSHEET puts results from a regression, generalized linear or nonlinear model into Genstat spreadsheets

Procedure in the Library relevant to regression analysis include:

    RCHECK checks the fit of a regression model
    RGRAPH draws a graph to display the fit of a regression model
    RDESTIMATES plots one- or two-way tables of regression estimates
    RPERMTEST does random permutation and exact tests for regression or generalized-linear-model analyses
    RPOWER calculates the power (probability of detection) for regression models
    RCOMPARISONS calculates comparison contrasts amongst the levels of a factor classifying a table of regression means
    RRETRIEVE retrieves a regression save structure from an external file
    RSTORE stores a regression save structure in an external file
    RTCOMPARISONS calculates comparison contrasts within a multi-way table of means
    RWALD calculates Wald and F tests for dropping terms from a regression
    RYPARALLEL fits the same regression model to several response variates, and collates the output
    SED2ESE calculates effective standard errors that give good approximate sed’s
    SEDLSI calculates least significant intervals
    LSIPLOT plots least significant intervals
    MCOMPARISON performs pairwise multiple comparison tests within a table of predictions
    BRDISPLAY displays a regression tree
    BREGRESSION constructs a regression tree
    BRPREDICT makes predictions using a regression tree
    BRVALUES forms values for nodes of a regression tree
    DILUTION calculates Most Probable Numbers from dilution series data
    EXTRABINOMIAL fits models to overdispersed proportions
    FIELLER calculates effective doses or relative potencies
    FITINDIVIDUALLY 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)
    FITMULTINOMIAL fits generalized linear models with multinomial distribution
    GEE fits models to longitudinal data by generalized estimating equations
    GLM analyses non-standard generalized linear models
    GLMM fits a generalized linear mixed model
    HGANALYSE analyses data using a hierarchical generalized linear model (HGLM) or a double hierarchical generalized linear model (DHGLM)
    HGDISPLAY displays results from an HGLM or DHGLM
    HGDRANDOMMODEL adds random terms into the dispersion models of an HGLM, so that the whole model becomes a DHGLM
    HGFIXEDMODEL defines the fixed model for an HGLM or DHGLM
    HGFTEST calculates likelihood tests for fixed terms in a hierarchical generalized linear model
    HGGRAPH draws a graph to display the fit of an HGLM or DHGLM analysis
    HGKEEP saves information from an HGLM or DHGLM analysis
    HGNONLINEAR defines nonlinear parameters for the fixed model of an HGLM
    HGPLOT produces model-checking plots for an HGLM or DHGLM
    HGPREDICT forms predictions from an HGLM or DHGLM analysis
    HGRANDOMMODEL defines the random model for an HGLM
    HGRTEST calculates likelihood tests for random terms in a hierarchical generalized linear model
    HGSTATUS displays the current HGLM model definitions
    HGWALD prints or saves Wald tests for fixed terms in an HGLM
    IFUNCTION estimates implicit and/or explicit functions of parameters
    MAREGRESSION does regressions for single-channel microarray data
    MINIMIZE finds the minimum of a function calculated by a procedure
    MIN1DIMENSION finds the minimum of a function in one dimension
    MICHAELISMENTEN fits the Michaelis-Menten equation for substrate concentration versus time data
    MMPREDICT predicts the Michaelis-Menten curve for a particular set of parameter values
    NLAR1 fits curves with an AR1 or a power-distance correlation model
    PAIRTEST performs t-tests for pairwise differences
    PPAIR displays results of t-tests for pairwise differences in compact diagrams
    PROBITANALYSIS fits probit models allowing for natural mortality and immunity
    R0INFLATED fits zero-inflated regression models to count data with excess zeros
    R0KEEP saves information from models fitted by R0INFLATED
    RAR1 fits regressions with an AR1 or a power-distance correlation model
    RBRADLEYTERRY fits the Bradley-Terry model for paired-comparison preference tests
 RCATENELSON performs a Cate-Nelson graphical analysis of bivariate data
    RCIRCULAR does circular regression of mean direction for an angular response
    RFINLAYWILKINSON performs Finlay and Wilkinson’s joint regression analysis of genotype-by-environment data
    RIDGE produces ridge regression and principal component regression analyses
    LRIDGE does logistic ridge regression
    RLASSO performs lasso using iteratively reweighted least-squares
    RQLINEAR fits and plots quantile regressions for linear models
    RQNONLINEAR fits and plots quantile regressions for nonlinear models
    RQSMOOTH fits and plots quantile regressions for loess or spline models
    RLFUNCTIONAL fits a linear functional relationship model
    RMGLM fits a model where different units follow different generalized linear models
    RNEGBINOMIAL fits a negative binomial generalized linear model estimating the aggregation parameter
    RNONNEGATIVE fits a generalized linear model with nonnegativity constraints (synonym FITNONNEGATIVE)
    RPAIR gives t-tests for all pairwise differences of means from linear or generalized linear models
    RPARALLEL carries out analysis of parallelism for nonlinear functions (synonym FITPARALLEL)
    RQUADRATIC fits a quadratic surface and estimates its stationary point
    RSCHNUTE fits a general four-parameter growth model to a non-decreasing response variate (synonym FITSCHNUTE)
    RSCREEN performs screening tests for generalized or multivariate linear models
    RSEARCH searches through models for a regression or generalized linear model (with methods including all-subsets, forward and backward stepwise regression)
    R2LINES fits two-straight-line (broken-stick) models to data
    SIMPLEX searches for the minimum of a function using the Nelder-Mead algorithm
    SVGLM fits generalized linear models to survey data
    WADLEY fits models for Wadley’s problem, allowing alternative links and errors
    XOCATEGORIES performs analyses of categorical data from crossover trials
    YTRANSFORM estimates the parameter lambda of a single parameter transformation
Updated on September 3, 2019

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