# Mixed Effects Regression Model: Mixed Effects Regression Model

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Mixed effects regression model Mixed-effects modeling is basically a regression technique which allows two kinds of effects: fixed effects (meaning just as in ordinary regression, intercepts and slopes intended to describe the population as a whole) and random effects (means the slopes and intercepts that can vary across subgroups of the sample). These models are useful in a wide variety of disciplines in the medical, biological and behavioral sciences. They are particularly useful in settings where measurements are repeated made on the same subject/unit under consideration (longitudinal study), or where measurements are taken on clusters of related subjects/units. Mixed-effects models open a wide array of possibilities for multilevel models,…show more content…
Rasbash provided several reasons to prefer a mixed effects model over a traditional fixed effects regression model. Firstly, if we wish to estimate the effect of covariates at the group level, it is not possible to sort out group effects from the effect of covariates at the group level by applying simply a fixed effects model. Secondly, random effects models consider the grouping variable as a random sample from a population of groups. But, the results cannot be generalized beyond the groups in the sample in a fixed effects model. Thirdly, statistical inference may be wrong. The traditional regression techniques do not make out the multilevel structure and will cause the standard errors of regression coefficients to be estimated erroneously. It will lead to an overstatement or understatement of statistical significance for the coefficients of higher level as well as lower level…show more content…
While there has been considerable interest in mixed-effects models for longitudinal and hierarchical, clustered, or multi-level measurement data, there has been less focus on mixed-effects models for discrete data. Stiratelli et. al. (1984) developed a mixed-effects logit model for modeling correlated binary data and Gibbons and Bock (1987) developed a more general mixed-effects probit model for similar applications. Gibbons et. al. (1994) and Gibbons and Hedeker (1994) further generalized the mixed-effects probit model for application to multiple time-varying and time-invariant covariates and alternate response functions and prior distributions. Making use of quasi-likelihood estimation methods in which there is no assumption about the distributional form assumed for the outcome measure, Liang and Zeger (1986) and Zeger and Liang (1986) explained that consistent estimates of variance and regression parameters can be obtained regardless of the dependency on time. Koch et. al. (1977) and Goldstein (1991) have illustrated how random effects can be incorporated into log-linear models. Wong and Mason (1985) proposed the generalizations of the logistic regression model in which the values of all regression coefficients vary randomly over individuals (Gibbons & Hedeker, 1994). These models can be applied to both longitudinal as