# World Journal of Probability and Statistics Research

## Current Issue

Vol. 2, No. 3, September 2016

### Articles

Expectation and Maximization Algorithm for Estimation in Random and Fixed Effect Model in Mixed Model

ABSTRACT

Several response variables were categorized only two groups or classes in every subject classified observations on being successful or unsuccessful. Such conditions tend to the binomial distribution. Binomial distribution is often found in the response variables are correlated to longitudinal data. Longitudinal data with binomial distributed response variables can be modeled in Mixed Model. Mixed Model used to model the longitudinal data on clinical research and epidemiological studies such as cancer and other diseases. The purpose of this study was to test whether the algorithm Expectation Maximization (EM) to estimate model parameters Mixed Model better than commonly used algorithms that Newton Rhapson (NR) algorithm. This study uses four simulation of data in health research. Based on the research data, it can be concluded that the EM algorithm to estimate the parameters better than the models Mixed Model NR algorithm.

Keywords: Mixed Model, EM algorithm, and the algorithm NR

GENERALIZED PENALIZED SPLINE NONPARAMETRIC REGRESSION APPROACH INBIRESPONSELONGITUDINAL

ABSTRACT

Longitudinal data are derived from observations conducted to nsubjects that are independent, observed repeatedly (repeated measurement) within a certain time.In longitudinal data of health sector, it is frequently found more than one response variable of repeated observations results on subjects that are similar, so that the proper data analysis is the analysis of biresponse longitudinal data. The purpose of this study is to establish the longitudinal equation with Generalized Penalized Spline (GPS) approach.The data were obtained from a study conducted by Fernandes and Wardhani (2008),thatwas the data of patients suffering Decubitus Wound with the response of wound extent on hands and wound extent on body. The longitudinal data equation using the approach of GPS biresponse results in the best estimator when usingknotat 1 with polynomial of degree 2 (quadratic) with GCV = 1983,417 and R2equal to 97.829% and 98.119%.

Keywords: Longitudinal Data, GPS, biresponse