VGAM-package              package:VGAM              R Documentation

_V_e_c_t_o_r _G_e_n_e_r_a_l_i_z_e_d _L_i_n_e_a_r _a_n_d _A_d_d_i_t_i_v_e _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n:

     Vector generalized linear and additive models, and associated
     models (Reduced-Rank VGLMs, Quadratic RR-VGLMs, Reduced-Rank
     VGAMs). This package fits many models and distribution by maximum
     likelihood estimation (MLE) or penalized MLE. Also fits
     constrained ordination models in ecology.

_D_e_t_a_i_l_s:


       Package:   VGAM
       Version:   0.7-1
       Date:      2006-10-24
       Depends:   R (>= 2.4.0), splines, methods, stats, stats4
       License:   GPL version 2
       URL:       http://www.stat.auckland.ac.nz/~yee/VGAM
       LazyLoad:  yes
       LazyData:  yes
       Packaged:  Tue Oct 24 15:36:03 2006; yee
       Built:     R 2.4.0; i686-pc-linux-gnu; 2006-10-24 15:44:11; unix

     Index:


     AA.Aa.aa                The AA-Aa-aa Blood Group System
     AB.Ab.aB.ab             The AB-Ab-aB-ab Blood Group System
     AB.Ab.aB.ab2            The AB-Ab-aB-ab2 Blood Group System
     ABO                     The ABO Blood Group System
     Benini                  The Benini Distribution
     Betabin                 The Beta-Binomial Distribution
     Betageom                The Beta-Geometric Distribution
     Betanorm                The Beta-Normal Distribution
     Bisa                    The Birnbaum-Saunders Distribution
     Brat                    Inputting Data to fit a Bradley Terry
     Model
     Coef                    Computes Model Coefficients and Quantities
     Coef.qrrvglm            Returns Important Matrices etc. of a QO
     Object
     Coef.qrrvglm-class      Class "Coef.qrrvglm"
     Coef.rrvglm             Returns Important Matrices etc. of a
     RR-VGLM
                             Object
     Coef.rrvglm-class       Class "Coef.rrvglm"
     Coef.vlm                Extract Model Coefficients for VLM Objects
     Dagum                   The Dagum Distribution
     Fisk                    The Fisk Distribution
     Frank                   Frank's Bivariate Distribution
     Frechet                 The Frechet Distribution
     G1G2G3                  The G1G2G3 Blood Group System
     Hzeta                   Haight's Zeta Function
     Inv.gaussian            The Inverse Gaussian Distribution
     Invlomax                The Inverse Lomax Distribution
     Invparalogistic         The Inverse Paralogistic Distribution
     Links                   Link functions for VGLM/VGAM/etc. families
     Lino                    The Generalized Beta Distribution (Libby
     and
                             Novick, 1982)
     Log                     Logarithmic Distribution
     Lomax                   The Lomax Distribution
     MNSs                    The MNSs Blood Group System
     Max                     Maxima
     Maxwell                 The Maxwell Distribution
     Nakagami                Nakagami Distribution
     Opt                     Maxima
     Paralogistic            The Paralogistic Distribution
     Pareto                  The Pareto Distribution
     ParetoIV                The Pareto(IV/III/II) Distributions
     Polono                  The Poisson Lognormal Distribution
     Posbinom                Positive-Binomial Distribution
     Posnorm                 The Positive-Normal Distribution
     Pospois                 Positive-Poisson Distribution
     Rayleigh                The Rayleigh Distribution
     Sinmad                  The Singh-Maddala Distribution
     Tikuv                   A Short-tailed Symmetric Distribution
     Tol                     Tolerances
     Tpareto                 The Truncated Pareto Distribution
     Zeta                    The Zeta Distribution
     Zibinom                 Zero-Inflated Binomial Distribution
     Zipf                    The Zipf Distribution
     Zipois                  Zero-Inflated Poisson Distribution
     acat                    Ordinal Regression with Adjacent
     Categories
                             Probabilities
     auuc                    Auckland University Undergraduate Counts
     benini                  Benini Distribution Family Function
     betaII                  Beta Distribution of the Second Kind
     betabin.ab              Beta-binomial Distribution Family Function
     betabinomial            Beta-binomial Distribution Family Function
     betaff                  The Two-parameter Beta Distribution Family
                             Function
     betageometric           Beta-geometric Distribution Family
     Function
     betaprime               The Beta-Prime Distribution
     bilogis4                Bivariate Logistic Distribution
     bilogistic4             Bivariate Logistic Distribution Family
     Function
     binom2.or               Bivariate Logistic Regression
     binom2.rho              Bivariate Probit Model
     binomialff              Binomial Family Function
     bisa                    Birnbaum-Saunders Distribution Family
     Function
     bminz                   Body Mass Index of New Zealand Adults
     brat                    Bradley Terry Model
     bratt                   Bradley Terry Model With Ties
     calibrate               Model Calibrations
     calibrate.qrrvglm       Calibration for CQO, UQO and CAO models
     calibrate.qrrvglm.control
                             Control function for CQO/UQO/CAO
     calibration
     cao                     Fitting Constrained Additive Ordination
     (CAO)
     cao.control             Control Function for RR-VGAMs (CAO)
     cauchit                 Cauchit Link Function
     cauchy1                 Cauchy Distribution Family Function
     ccoef                   Extract Model Constrained/Canonical
                             Coefficients
     cdf.lmscreg             Cumulative Distribution Function for LMS
                             Quantile Regression
     cexpon                  Censored Exponential Distribution
     cgo                     Redirects the user to cqo
     cgumbel                 Censored Gumbel Distribution
     chest                   Chest Pain in NZ Adults
     chisq                   Chi-squared Distribution
     clo                     Redirects the user to rrvglm
     cloglog                 Complementary Log-log Link Function
     cnormal1                Censored Normal Distribution
     coalminers              Breathlessness and Wheeze Amongst
     Coalminers
     constraints             Constraint Matrices
     cqo                     Fitting Constrained Quadratic Ordination
     (CQO)
     cratio                  Ordinal Regression with Continuation
     Ratios
     cumulative              Ordinal Regression with Cumulative
                             Probabilities
     dagum                   Dagum Distribution Family Function
     dcnormal1               Univariate Normal Distribution with Double
                             Censoring
     deplot.lmscreg          Density Plot for LMS Quantile Regression
     dgumbel                 The Gumbel Distribution
     dirichlet               Fitting a Dirichlet Distribution
     dirmul.old              Fitting a Dirichlet-Multinomial
     Distribution
     dirmultinomial          Fitting a Dirichlet-Multinomial
     Distribution
     dlaplace                The Laplace Distribution
     enzyme                  Enzyme data
     erf                     Error Function
     erlang                  Erlang Distribution
     expexp                  Exponentiated Exponential Distribution
     expexp1                 Exponentiated Exponential Distribution
     exponential             Exponential Distribution
     fff                     F Distribution Family Function
     fill                    Creates a Matrix of Appropriate Dimension
     fisherz                 Fisher's Z Link Function
     fisk                    Fisk Distribution family function
     fitted.vlm              Fitted Values of a VLM object
     frank                   Frank's Bivariate Distribution Family
     Function
     frechet2                Frechet Distribution Family Function
     freund61                Freund's (1961) Bivariate Extension of the
                             Exponential Distribution
     gamma1                  1-parameter Gamma Distribution
     gamma2                  2-parameter Gamma Distribution
     gamma2.ab               2-parameter Gamma Distribution
     gammahyp                Gamma Hyperbola Bivariate Distribution
     garma                   GARMA (Generalized Autoregressive
                             Moving-Average) Models
     gaussianff              Gaussian (normal) Family Function
     genbetaII               Generalized Beta Distribution of the
     Second
                             Kind
     genpoisson              Generalized Poisson distribution
     geometric               Geometric Distribution
     get.smart               Retrieve One Component of
     ".smart.prediction"
     get.smart.prediction    Retrieves ".smart.prediction"
     gev                     Generalized Extreme Value Distribution
     Family
                             Function
     gevUC                   The Generalized Extreme Value Distribution
     gew                     General Electric and Westinghouse Data
     ggamma                  Generalized Gamma distribution family
     function
     ggammaUC                The Generalized Gamma Distribution
     golf                    Gamma-Ordinal Link Function
     gpd                     Generalized Pareto Distribution Family
     Function
     gpdUC                   The Generalized Pareto Distribution
     grc                     Fitting Goodman's RC Association Model
     gumbel                  Gumbel Distribution Family Function
     guplot                  Gumbel Plot
     hspider                 Hunting Spider Data
     hunua                   Hunua Ranges data
     hyper                   Hypergeometric Family Function
     hzeta                   Haight's Zeta Family Function
     iam                     Index from Array to Matrix
     identity                Identity Link Function
     inv.gaussianff          Inverse Gaussian Distribution Family
     Function
     invlomax                Inverse Lomax Distribution Family Function
     invparalogistic         Inverse Paralogistic Distribution Family
                             Function
     is.smart                Test For a Smart Object
     leipnik                 Leipnik Distribution Family Function
     lerch                   Lerch Phi Function
     levy                    Levy Distribution Family Function
     lgammaUC                The Log-Gamma Distribution
     lgammaff                Log-gamma Distribution Family Function
     lino                    Generalized Beta Distribution Family
     Function
     lirat                   Low-iron Rat Teratology Data
     lms.bcg                 LMS Quantile Regression with a Box-Cox
                             transformation to a Gamma Distribution
     lms.bcn                 LMS Quantile Regression with a Box-Cox
                             Transformation to Normality
     lms.yjn                 LMS Quantile Regression with a Yeo-Johnson
                             Transformation to Normality
     logc                    Complementary-log Link Function
     loge                    Log link function
     logff                   Logarithmic Distribution
     logistic                Logistic Distribution Family Function
     logit                   Logit Link Function
     loglinb2                Loglinear Model for Two Binary Responses
     loglinb3                Loglinear Model for Three Binary Responses
     loglog                  Log-log Link Function
     lognormal               Lognormal Distribution
     logoff                  Log link function with an offset
     lomax                   Lomax Distribution Family Function
     lv                      Latent Variables
     lvplot                  Latent Variable Plot
     lvplot.qrrvglm          Latent Variable Plot for QO models
     lvplot.rrvglm           Latent Variable Plot for RR-VGLMs
     maxwell                 Maxwell Distribution Family Function
     mccullagh89             McCullagh (1989) Distribution Family
     Function
     mckaygamma2             McKay's Bivariate Gamma Distribution
     meplot                  Mean Excess Plot
     micmen                  Michaelis-Menten Model
     mix2normal1             Mixture of Two Univariate Normal
     Distributions
     mix2poisson             Mixture of Two Poisson Distributions
     model.framevlm          Construct the Model Frame of a VLM Object
     model.matrixvlm         Construct the Design Matrix of a VLM
     Object
     multinomial             Multinomial Logit Model
     nakagami                Nakagami Distribution Family Function
     nbolf                   Negative Binomial-Ordinal Link Function
     negbinomial             Negative Binomial Distribution Family
     Function
     normal1                 Univariate normal distribution
     notdocumentedyet        Undocumented and Internally Used Functions
     and
                             Classes
     nzc                     Chinese Population in New Zealand
     1867-2001
     oxtemp                  Oxford Temperature Data
     paralogistic            Paralogistic Distribution Family Function
     pareto1                 Pareto and Truncated Pareto Distribution
     Family
                             Functions
     paretoIV                Pareto(IV/III/II) Distribution Family
     Functions
     persp.qrrvglm           Perspective plot for QRR-VGLMs
     plotdeplot.lmscreg      Density Plot for LMS Quantile Regression
     plotqrrvglm             Model Diagnostic Plots for QRR-VGLMs
     plotqtplot.lmscreg      Quantile Plot for LMS Quantile Regression
     plotvgam                Default VGAM Plotting
     plotvgam.control        Control Function for plotvgam()
     pneumo                  Pneumoconiosis amongst a group of
     coalminers
     poissonff               Poisson Family Function
     polf                    Poisson-Ordinal Link Function
     posbinomial             Positive Binomial Distribution Family
     Function
     posnegbinomial          Positive Negative Binomial Distribution
     Family
                             Function
     posnormal1              Positive Normal Distribution Family
     Function
     pospoisson              Positive Poisson Distribution Family
     Function
     predict.vglm            Predict Method for a VGLM fit
     prentice74              Prentice (1974) Log-gamma Distribution
     probit                  Probit Link Function
     put.smart               Adds a List to the End of the List
                             ".smart.prediction"
     qrrvglm.control         Control function for QRR-VGLMs (CQO)
     qtplot.gumbel           Quantile Plot for Gumbel Regression
     qtplot.lmscreg          Quantile Plot for LMS Quantile Regression
     quasibinomialff         Quasi-Binomial Family Function
     quasipoissonff          Quasi-Poisson Family Function
     rayleigh                Rayleigh Distribution Family Function
     rcqo                    Constrained Quadratic Ordination
     rdiric                  The Dirichlet distribution
     recexp1                 Upper Record Values from a 1-parameter
                             Exponential Distribution
     reciprocal              Reciprocal link function
     recnormal1              Upper Record Values from a Univariate
     Normal
                             Distribution
     rhobit                  Rhobit Link Function
     rig                     Reciprocal Inverse Gaussian distribution
     rlplot.egev             Return Level Plot for GEV Fits
     rposnegbin              Positive-negative binomial distribution
     random
                             variates
     rrar                    Nested reduced-rank autoregressive models
     for
                             multiple time series
     rrvglm                  Fitting Reduced-Rank Vector Generalized
     Linear
                             Models (RR-VGLMs)
     rrvglm-class            Class "rrvglm"
     rrvglm.control          Control function for rrvglm
     rrvglm.optim.control    Control function for rrvglm() calling
     optim()
     s                       Defining smooths in VGAM formulae
     setup.smart             Smart Prediction Setup
     simplex                 Simplex distribution
     sinmad                  Singh-Maddala Distribution Family Function
     skewnormal1             Univariate Skew-Normal Distribution Family
                             Function
     smart.expression        S Expression for Smart Functions
     smart.mode.is           Determine What Mode the Smart Prediction
     is In
     smartpred               Smart Prediction
     snorm                   Skew-Normal Distribution
     sratio                  Ordinal Regression with Stopping Ratios
     studentt                Student t Distribution
     tikuv                   Short-tailed Symmetric Distribution Family
                             Function
     tobit                   Tobit Model
     trplot                  Trajectory Plot
     trplot.qrrvglm          Trajectory plot for QRR-VGLMs
     uqo                     Fitting Unconstrained Quadratic Ordination
                             (UQO)
     uqo.control             Control Function for UQO models
     usagrain                USA grain prices
     venice                  Venice Maximum Sea Levels
     vgam                    Fitting Vector Generalized Additive Models
     vgam-class              Class "vgam"
     vgam.control            Control function for vgam
     vglm                    Fitting Vector Generalized Linear Models
     vglm-class              Class "vglm"
     vglm.control            Control function for vglm
     vglmff-class            Class "vglmff"
     vonmises                von Mises Distribution Family Function
     vsmooth.spline          Vector cubic smoothing spline
     waitakere               Waitakere Ranges data
     wald                    Wald Distribution Family Function
     weibull                 Weibull Distribution Family Function
     weightsvglm             Prior and Working Weights of a VGLM fit
     wrapup.smart            Cleans Up After Smart Prediction
     yeo.johnson             Yeo-Johnson Transformation
     yip88                   Zero-Inflated Poisson Distribution (Yip
     (1988)
                             algorithm)
     zanegbinomial           Zero-Altered Negative Binomial
     Distribution
     zapoisson               Zero-Altered Poisson Distribution
     zero                    The zero Argument in VGAM Family Functions
     zeta                    Riemann's Zeta Function
     zetaff                  Zeta Distribution Family Function
     zibinomial              Zero-Inflated Binomial Distribution Family
                             Function
     zipf                    Zipf Distribution Family Function
     zipoisson               Zero-Inflated Poisson Distribution Family
                             Function


_A_u_t_h_o_r(_s):

     Thomas W. Yee <t.yee@auckland.ac.nz>

     Maintainer: Thomas Yee <t.yee@auckland.ac.nz>

_R_e_f_e_r_e_n_c_e_s:

     Yee, T. W. and Hastie, T. J. (2003) Reduced-rank vector
     generalized linear models. _Statistical Modelling_, *3*, 15-41.

     Yee, T. W. and Wild, C. J. (1996) Vector generalized additive
     models. _Journal of the Royal Statistical Society, Series B,
     Methodological_, *58*, 481-493.

     Yee, T. W. (2004) A new technique for maximum-likelihood canonical
     Gaussian ordination. _Ecological Monographs_, *74*, 685-701.

     Yee, T. W. (2006) Constrained additive ordination. _Ecology_,
     *87*, 203-213.

_E_x_a_m_p_l_e_s:

     # Fit the proportional odds model, p.179, in McCullagh and Nelder (1989)
     data(pneumo)
     pneumo = transform(pneumo, let=log(exposure.time))
     (fit = vglm(cbind(normal, mild, severe) ~ let,
                 cumulative(parallel=TRUE, reverse=TRUE), pneumo))
     fit@y   # Sample proportions
     weights(fit, type="prior")   # Number of observations
     coef(fit, matrix=TRUE)
     constraints(fit)   # Constraint matrices

     # Fit a two species GAM simultaneously
     data(hunua)
     fit2 = vgam(cbind(agaaus, kniexc) ~ s(altitude),
                 fam = binomialff(mv=TRUE), hunua)
     coef(fit2, mat=TRUE)   # Not really interpretable
     ## Not run: 
     plot(fit2, se=TRUE, overlay=TRUE, lcol=1:2, scol=1:2)
     attach(hunua)
     o = order(altitude)
     matplot(altitude[o], fitted(fit2)[o,], type="l", lwd=2, las=1,
         xlab="Altitude (m)", ylab="Probability of presence",
         main="Two plant species' response curves", ylim=c(0,.8))
     rug(altitude)
     detach(hunua)
     ## End(Not run)


     # LMS quantile regression
     data(bminz)
     fit = vgam(BMI ~ s(age, df=c(4,2)), fam=lms.bcn(zero=1), data=bminz, tr=TRUE)
     predict(fit)[1:3,]
     fitted(fit)[1:3,]
     bminz[1:3,]
     # Person 1 is near the lower quartile of BMI amongst people his age
     cdf(fit)[1:3]

     ## Not run: 
     # Quantile plot
     par(bty="l", mar=c(5,4,4,3)+0.1, xpd=TRUE)
     qtplot(fit, percentiles=c(5,50,90,99), main="Quantiles",
            xlim=c(15,90), las=1, ylab="BMI", lwd=2, lcol=4)

     # Density plot
     ygrid = seq(15, 43, len=100)  # BMI ranges
     par(mfrow=c(1,1), lwd=2)
     a = deplot(fit, x0=20, y=ygrid, xlab="BMI", col="black",
         main="Density functions at Age = 20 (black), 42 (red) and 55 (blue)")
     a
     a = deplot(fit, x0=42, y=ygrid, add=TRUE, llty=2, col="red")
     a = deplot(fit, x0=55, y=ygrid, add=TRUE, llty=4, col="blue", Attach=TRUE)
     a@post$deplot  # Contains density function values
     ## End(Not run)

     # GEV distribution for extremes
     data(oxtemp)
     (fit = vglm(maxtemp ~ 1, egev, data=oxtemp, trace=TRUE))
     fitted(fit)[1:3,]
     coef(fit, mat=TRUE)
     Coef(fit)
     vcov(fit)
     vcov(fit, untransform=TRUE)
     sqrt(diag(vcov(fit)))   # Approximate standard errors
     ## Not run:  rlplot(fit) 

