# Fits a marginal model using IPW provides inverse probability weighted estimates of parameters for semiparametric marginal model of response variable of interest. The weights are computed using a generalized linear mixed effect model. ```r lmeipw( data, M = 5, id, analysis.model, wgt.model, qpoints = 4, nu, sigmaR, dist, link, conv = 1e-04, maxiter, maxpiinv = -1, se = TRUE, verbose = FALSE ) ``` ## Arguments - `data`: longitudinal data with each subject specified discretely - `M`: number of imputation to be used in the estimation of augmentation term - `id`: cloumn names which shows identification number for each subject - `analysis.model`: A formula to be used as analysis model - `wgt.model`: Formula for weight model, which consider subject specific random intercept - `qpoints`: Number of quadrature points to be used while evaluating the numerical integration - `nu`: working model parameter - `sigmaR`: working model parameter - `dist`: distribution for imputation model. Currently available options are Gaussian, Binomial - `link`: Link function for the mean - `conv`: convergence tolerance - `maxiter`: maximum number of iteration - `maxpiinv`: maximum value pi can take - `se`: Logical for Asymptotic SE for regression coefficient of the regression model. - `verbose`: logical argument ## Returns A list of objects containing the following objects - **Call**: details about arguments passed in the function - **nr.conv**: logical for checking convergence in Newton Raphson algorithm - **nr.iter**: number of iteration required - **nr.diff**: absolute difference for roots of Newton Raphson algorithm - **beta**: estimated regression coefficient for the analysis model - **var.beta**: Asymptotic SE for beta ## Details lmeipw It uses the simple inverse probability weighted method to reduce the bias due to missing values in response model for longitudinal data.The response variable $\mathbf{Y}$ is related to the covariates as $g(\mu)=\mathbf{X}\beta$, where `g` is the link function for the glm. The estimating equation is $$ \sum_{i=1}^{n}\sum_{j=t_1}^{t_k}\int_{a_i}\frac{\delta_{ij}}{\hat\pi_{ij}(a_i)}S(Y_{ij},\mathbf{X}_{ij})da_i=0 $$ where $\delta_{ij}=1$ if there is missing no value in response and 0 otherwise. $\mathbf{X}$ is fully observed all subjects and for the missing data probability $$ Logit(P(\delta_{ij}=1|\mathbf{V}_{ij}\nu+a_i))\;;a_i\sim N(0,\sigma_R) $$ ; where $\mathbf{V}_{ij}=(\mathbf{X}_{ij},A_{ij})$ ## Examples ```r ## Not run: ## library(JMbayes2) library(lme4) library(insight) library(numDeriv) library(stats) lmer(log(alkaline)~drug+age+year+(1|id),data=na.omit(pbc2)) data1<-pbc2 data1$alkaline<-log(data1$alkaline) names(pbc2) apply(pbc2,2,function(x){sum(is.na(x))}) r.ij<-ifelse(is.na(data1$alkaline)==T,0,1) data1<-cbind.data.frame(data1,r.ij) data1$drug<-factor(data1$drug,levels=c("placebo","D-penicil"),labels = c(0,1)) data1$sex<-factor(data1$sex,levels=c('male','female'),labels=c(1,0)) data1$drug<-as.numeric(as.character(data1$drug)) data1$sex<-as.numeric(as.character(data1$sex)) r.ij~year+age+sex+drug+serBilir+(1|id) model.r<-glmer(r.ij~year+age+sex+drug+serBilir+(1|id),family=binomial(link='logit'),data=data1) nu<-model.r@beta sigmaR<-get_variance(model.r)$var.random m11<-lmeipw(data=data1,id='id', analysis.model = alkaline~year, wgt.model=~year+age+sex+drug+serBilir+(1|id), nu=nu,sigmaR=sigmaR,dist='gaussian',link='identity',qpoints=4, maxiter = 200) m11 ## ## End(Not run) ``` ## References Wang, C. Y., Shen-Ming Lee, and Edward C. Chao. "Numerical equivalence of imputing scores and weighted estimators in regression analysis with missing covariates." Biostatistics 8.2 (2007): 468-473. Seaman, Shaun R., and Stijn Vansteelandt. "Introduction to double robust methods for incomplete data." Statistical science: a review journal of the Institute of Mathematical Statistics 33.2 (2018): 184. Vansteelandt, Stijn, James Carpenter, and Michael G. Kenward. "Analysis of incomplete data using inverse probability weighting and doubly robust estimators." Methodology: European Journal of Research Methods for the Behavioral and Social Sciences 6.1 (2010): 37. ## See Also SIPW ,miSIPW ,miAIPW ## Author(s) Atanu Bhattacharjee, Bhrigu Kumar Rajbongshi and Gajendra Kumar Vishwakarma

lmeipw function