Major components of GLMs

• a probability distribution for the response variable, 
• a linear predictor function of the predictor variables, and 
• a link function that connects the linear predictor to the response variable’s mean. 

The probability distribution and link function used is determined by the type of response variable and the research topic at hand. R includes methods for fitting GLMs, such as the glm() function. The user can specify the formula for the model, which contains the response variable and one or more predictor variables, as well as the probability distribution and link function to be used, using this function.

Mathematical Analysis of GLM

A statistical structure known as GLM (Generalized Linear Models) expands the capabilities of the linear regression model to account for non-normal response variables. Defining a probability distribution for the response variable and modelling the correlation between the predictor variables and the response variable’s expected value make up the quantitative analysis of GLM.
Let X be a matrix of predictor factors, and let Y be the response variable. We presume that Y has a normal distribution with mean and variance 2 in a linear regression model. Following that, the connection between Y and X is modelled as:

                                   Y = Xβ + ε

where is a vector of regression coefficients and is a vector of errors that are normally distributed and have a mean and range of 0 and 2, respectively.
We permit non-normal populations in GLM.

                                  g(μ) = Xβ
                                  Var(Y) = φV(μ)

where V() is a variance function from the exponential family, Var(Y) is the variance of Y, g() is the link function, is the expected value of Y, is a scale parameter, and is the link parameter.
to calculate the parameter values for and. By maximising the likelihood function, the maximum likelihood approximation of is obtained:

                                    L(x, y | x, y) = i=1n f(yi | i, y)

where i is the anticipated value of Yi for the ith observation and f() is the probability density function of the exponential family distribution.

GLM stands for Generalized Linear Models in R Programming Language. It is a flexible framework used in various statistical models, including linear regression, logistic regression, Poisson regression, and many others.

GLMs (Generalized linear models) are a type of statistical model that is extensively used in the analysis of non-normal data, such as count data or binary data. They enable us to describe the connection between one or more predictor variables and a response variable in a flexible manner. This tutorial will go over how to create generalized linear models in the R Programming Language.