Applying generalized linear models in STATA
Generalized linear models (GLM) are the conventional linear models used in continuous response variables that have categorical and/or continuous variables. They include linear regression, analysis of variance, log linear models, ANCOVA, Poisson regression, logistic regression, and multinomialresponse. Although these models can be fit in STATA using logit and other specialized commands, fitting them using the STATA’s glmcodehas been found to offer some benefits. For instance, one can calculate and interpret model diagnosticsirrespective of the assumed distribution. Read on to find out how generalized linear models are applied to STATA as explained by our generalized linear models assignment help experts.
Components of GLM applied by our STATA homework help professionals
There are three major components of generalized linear models fitted in STATA. Our STATA homework help experts have listed them below:
1. Linear predictor
A linear predictor refers to the linear combination of a parameter and an explanatory variable. The parameter is usually denoted as b and the explanatory variable is usually given the value x.
2. Link function
A link function generally joins the parameter and the linear predictor together in a probability distribution. There are different link functions for different statistical models. For instance, in Poisson regression, the link function would be the log link function.
3. Probability distribution
Probability distribution in STATA can be defined as the list of all the outcomes that are likely to be obtained from random variables including their corresponding probability values. It can be discrete, univariate, or finite.
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Learn the assumptions of GLM
When applying generalized linear models in STATA or any other statistical software, there are several assumptions that must be observed in order to give the best deliverables. Here are some of these assumptions highlighted by our STATA homework help experts:
- The data must be independently distributed, that is, all the cases should be independent.
- The dependent variable doesn’t need to be normally distributed; it will typically assume a binomial, multinomial, Poisson, or any other distribution based on how the data being observed is distributed.
- General linear models do not assume linear relationships between independent variables and dependent variables. Instead, they form a linear relationship between explanatory variables and the link function.
- The variance homogeneity need not be met. In fact, having homogeneity of variance is not even possible in generalized linear models in most cases because of over-dispersion as well as the structure of the models.
- Errors should be independent but not necessarily normally distributed.
- Generalized linear models use maximum likelihood estimations instead of the ordinary least squares in the estimation of parameters, which means, they can be used to make larger sample approximations.
- The goodness of fit measures in generalized linear models rely on sufficiently large numbers.
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