Abstract
Generalized linear models (GLMs) form a class of fixed effects regression models for several types of dependent variable, whether continuous, dichotomous or counts. Common GLMs include linear regression, Logistic regression and Poison regression. These models have typically been used a lot in modeling of data arising from a heterogeneous population under the assumption of independence. However, in applied science and in real life situations in general, one is confronted with collection of correlated data (Mark Aerts et al, 2005). This generic term embraces a multitude of data structures, such as multivariate observations, clustered data, repeated measurements, longitudinal data, and spatially correlated data. Generalized Linear Mixed Models (GLMMs) are able to handle extraordinary range of complications in regression-type analyses. They are often used to handle correlations that arise in longitudinal and other clustered data. This study sought to fit GLMMs to Kenya integrated household data collected in 2005/6 to explain different factors and their influence on an individual morbidity in Kenya. The cluster variable was used to introduce the random effect in this data. From the analysis, it was deduced that gender increases the log-odds of an individual getting a disease, while people who are living in good housing conditions reduces the log-odds of an individual experiencing morbidity. Main source of drinking water and the human waste disposal method were significant in explaining individual morbidity in Kenya. This study can however be extended to incorporate other factors such as income level of individuals. Individuals with low level of income are believed to be more likely to experience environmental health related diseases than individuals with higher levels of income.
Highlights
Generalized Linear Mixed Models (GLMMs) extend the generalized linear model, as proposed by Nelder and Wedderburn (1972) and comprehensively described in Mc Cullaghand Nelder (1989), by adding normally distributed random effects on the linear predictor scale in order to include the concept of correlated data such as clustered data
GLMM is one of the most useful structures in modern statistics, allowing many complications to be handled within the familiar linear model framework
This study showed that the family and the community random effects were statistically significant in both models; unobserved family effects were far more important than unobserved community effects
Summary
Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data type. GLMMs extend the generalized linear model, as proposed by Nelder and Wedderburn (1972) and comprehensively described in Mc Cullaghand Nelder (1989), by adding normally distributed random effects on the linear predictor scale in order to include the concept of correlated data such as clustered data. GLMM is one of the most useful structures in modern statistics, allowing many complications to be handled within the familiar linear model framework. The fitting of such models has been the subject of a great deal of research over the past decade. Contributions to fitting various forms of the GLMM include Stiratelli, Laird and Ware (1984), Anderson and Aitkin (1985), Gilmour, Anderson and Rae (1985), Schall (1991), and Breslow and Clayton (1993)
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