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Longit Informatics Center:
A platform for online statistical data analysis

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**lm: Linear Models**
Linear Models (LM) are the standard approaches to study the relationship between a continuous response and a set of covariates. The model assumes the relationship is linear in parameters and the error term follows a normal distribution.**glm: Generalized Linear Models**
Generalized Linear Models (GLM) are extensions of modeling approaches for binary, count and continuous data. Such data may be assumed to follow the exponential family, e.g. binomial, Poissoin and Gamma distributions, etc. The GLM requires a link function to specify the relationship between the mean of the response and a set of predictors, i.e. covariates. **lme: Linear Mixed-effects Models**
Linear Mixed-effects (LME) Models are applicable for analyzing correlated continuous data, where there exist within-subject correlation and between-subject variations. An LME model applies a set of random effects to adjust the heterogeneity and dispersion, and it is applicable to high-dimensional hierarchical data such as panel surveys, longitudinal data, and profile data, etc.**do.lme: Linear Mixed-effects Models for Dropout Data**
For longitudinal data, it is very common that some subjects will be lost to follow up. If the mechanism of missing is unrelated to the outcome processes, there is little to worry about the analytic results. If the cause of missing is related to the outcomes, the estimating results might be under or over estimated. A selection model can be applied to jointly model the response of interest and the missing indicator. For continuous response, the response model could be an LME model and the missing indicator could be a logistic regression. Some parameters in the logit can indicate whether the missing mechanism is ignorable or missing not at random. Ultimately, you have to study the sensitivy analysis to evaluate the modeling assumption.

**glme: Generalized Linear Mixed-effects Models**
Generalized Linear Mixed-effects (GLME) Models are applicable for analyzing correlated data with discrete and continuous data, where there exist within-subject correlation and between-subject variations. This is an extension of LME to the exponential family. A GLME model applies a set of random effects to adjust the heterogeneity and dispersion, and it is applicable to high-dimensional hierarchical data such as panel surveys, longitudinal data, and profile data, etc.**mvm: Multivariate Multinomial Models**
The MVM module is applicable for the analysis of independent and correlated multivariate multinomial data. Several modeling approaches are available, and these are full likelihood methods, mixed-effects conditional likelihood methods, and marginal methods based on GEE modeling. Such modeling methods are extensions of the GLME and GEE methods for correlated binomial data to multinomial data, e.g. ordinal outcomes, customer satisfaction rating, achievement evaluation, and disease progression score, etc.**gee: Generalized Estimating Equations Models**
Generalized Estimating Equations (GEE) Models are applicable for analyzing correlated data with discrete and continuous data. The GEE models are robust methods, where only the first two moments are specified. Typically, the mean, variance, and their relationship from the exponential families are used in model specification, and a working correlation is used in constructing the estimating equations. As long as the estimating equations are unbiased, consistent results can be derived. Such modeling approaches are insufficient to specify the full likelihood, since the whole distribution function is not known. GEE methods are called quasi-likelihood methods and are comparable to GLME models. GLME models are full likelihood approaches and are conditional models for given random effects. The computation in GLME might involve likelihood approximations. GEE methods are marginal approaches, but random effects can be added to the mean structures, where the marginal variances might not have exact forms for some families.