BIMreg: Generalized Linear Mixed Models (GLMMs) for binomial data In idaejin/HRQoL: Health Related Quality of Life Analysis

Description

This model fits a logistic regression with Gaussian random effects. The random effects are assumed to be distributed as a normal distribution with zero mean.

Usage

 1 BIMreg(formula,n,random,data)

Arguments

 formula an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. n the maximum score of the binomial trials. random a vector containing the names of the random components in the data frame, the names must be between quotes. data an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula).

Details

The model that is performed by this function is a especial case of generalized linear mixed models (GLMMs), in which conditioned on some random components the response variable has a binomial distribution. As in the binomial (logistic) regression a logit link function is applied to the probability parameter of the conditioned distribution, allowing the inclusion of random components in the linear predictor,

logit(p)=Xβ+Zu,

where p is the probability parameter, X a full rank matrix composed by the covariables, β the regression coefficients, Z the design matrix for the random effects and u are the random effects. These random effects are independent and has a normal distribution with the same variance and mean 0.

The model estimates the fixed effects and the variance of the random effects, and predicts those random effects for each observation.

The estimation of the parameters is done by likelihood approximation, via iterative weighted least squares (IWLS) method. The estimation is performed in two steps: (i) fixed and random parameters are calculated for some given random component variances (ii) variances of the random effects are calculated for some given regression and random coefficients. The estimation approach iterates between (i) and (ii) until convergence is obtained.

Value

BImmreg returns an object of class "BIMreg".

The function summary (i.e., summary.BIMreg) can be used to obtain or print a summary of the results, coef can be used to print the regression coefficients of the model, fitted (i.e., fitted.BIMreg) to print the fitted values and residuals (i.e., residuals.BIMreg) to get the residuals.

 coefficients the estimated value of the fixed coefficients in the regression. coef.vcov the variance and covariance matrix of the estimated fixed coefficients in the regression. random.coef the predicted random effects of the regression. When more than one random effects are included the prediction of all the random coefficients is given, following the order defined in parameter random. random.var the variance of each random effect. deviance the deviance of the model based on the approximated log-likelihood. fitted.values the fitted mean values of the probability parameter of the conditioned binomial distribution, obtained by transforming the linear predictor by the inverse of the link function. residuals the residuals of the model. random.se the standard error of each random effect, the square of the variance of the random effects. working the final working vector of the iterative weighted least square method. iter the number of iterations in the estimation method. nObs the number of observations in the data. nrand the number of random components in the model. cluster the number of levels in each random component. y the dependent variable in the model. X the model matrix of the fixed effects. Z the model matrix of the random effects. D the variance and covariance matrix of the random effects. n the maximum score of the conditioned binomial trials. W the final weights matrix in the iterative weighted least square method. call the matched call. formula the formula supplied.

Author(s)

Josu Najera Zuloaga

Dae-Jin Lee

References

Breslow N. E. & Clayton D. G. (1993): Approximate Inference in Generalized Linear Mixed Models, Journal of the American Statistical Association, 88, 9-25.

McCulloch C. E. & Searle S. R. (2001): Generalized, Linear, and Mixed Models, John Wiley & Sons.

Pawitan Y. (2001): In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford University Press.

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 set.seed(5) # Create a dependent variable with a random covariable: nObs <- 500 x <- rnorm(nObs,4,1) id1 <- c(kronecker(seq(1,5),rep(1,100))) id2 <- c(kronecker(seq(1,10),rep(1,50))) p <- 1/(1+exp(-(5-5*x+kronecker(rnorm(5,0,0.5),rep(1,100))+kronecker(rnorm(10,0,1.2),rep(1,50))))) y <- rbinom(nObs,10,p) dat <- data.frame(cbind(y,x,id1,id2)) dat\$id1 <- as.factor(dat\$id1) dat\$id2 <- as.factor(dat\$id2) #Estimate the mixed model for one random component. mm1 <- BIMreg(y~x,10,c("id1"),dat) mm1 summary(mm1) #Estimate the mixed model for two random components. mm2 <- BIMreg(y~x,10,c("id1","id2"),dat) mm2 summary(mm2)

idaejin/HRQoL documentation built on May 18, 2019, 2:32 a.m.