General and Generalized Linear Models
The General Linear Model is a framework of statistical methods to relate some number of independent variables(IV) continuous and/or categorical variables(DV) to a single/Multiple Dependent Variable.
Some Example of GLM statistics models: ANOVA,T-test, Chi-Square, Linear Regression etc.
Generalized linear models (GLiM, or GLM)— Generalization of the linear regression model. Mean that rather than forcing a linear relationship between the dependent and independent variables, it allows the dependent variable to be related with the independent variables through a link function.
e.g., Poisson regression
Practical purpose of Generalized Linear Models: — The concept of GLM evolved when it was realized that not all the models can be handled with the Dependent variable varying in linear way.
e.g., When we normally run a regression it is assumed that Dependent variable is linearly with respect to independent variables. Now assume a case Y=X². Here response variable is quadratically related to independent variable.
Similarly there are many cases when response variable is exponentially or logarithmically related. That’s where we need generalized line.
Difference between general linear models and generalized linear models
The general linear model requires that the dependent variable follows the normal distribution whilst the generalized linear model is an extension of the general linear model that allows the specification of models whose response variable follows different distributions.
Components of GLM
Random/ Stochastic Component
Systematic Component
Link Function
Random/ Stochastic Component — Specifies the probability distribution of the response variable;
e.g., normal distribution for Dependent variable in the classical regression model, or binomial distribution for Dependent variable in the binary logistic regression model. This is the only random component in the model; there is not a separate error term.
Systematic Component — The systematic component of the model consists of a set of explanatory variables and some linear function of them.
Specifies the explanatory variables (x1, x2, x3,…,xn) in the model, more specifically, their linear combination (m0 + m1x1 + m2x2…).
This linear combination of our explanatory variables is referred to as a “linear predictor”.
Link Function — maps a non-linear relationship to a linear one. In simple words, it specifies the link between random and systematic components. It says how the expected value of the response relates to the linear predictor of explanatory variables. e.g., log, logit
In Future blog, I will come up with other parts of information.
Thank you for reading. Links to other blogs: —
The Poisson Distribution
The Geometric and Exponential Distributions
Uniform Distribution
Normal Distribution
Binomial Distribution
Central Limit Theorem
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