Types of Statistical Models

A relationship between variables in the form of mathematical equations is known as statistical model. It shows how one or more than one variables are related to the one or more variables.
Now we will see types of statistical models;
Generally there are two types of statistical model:
1. Lognormal statistical model;
2. Log Linear Regression model.
Here will see brief introduction about both the statistical model:
First we see lognormal statistical model:
Lognormal regression models are based on the statement that the natural Logarithm of P_i follows a normal distribution with Mean μ_i and variance G₂. In other words, it is understood that P_i follows a lognormal distribution, a choice whenever the data is
non - negative, signifying that a model with positive skew is needed and the mean is relatively large.
In this case, the relationship between the expected number of accidents at the i^th intersection and the ‘q’ predictor variables R1,...,Rq, can be given as:
Log (u_i) = β₀ + β₁ R_i1 + β₂ R_i2 +……+ β_q R_iq;
And in the multiplication form it can be written as:
u_i = exp (β₀)  exp (β₁ R_i1) exp (β₂ R_i1)…… exp (β_q R_iq);
Where, log is the normal distribution with mean μ_i and variance.
Now we will see log linear regression model;
The two log linear models are measured for application: the Poisson and the negative binomial models. The general forms are as follows:
The relationship between the estimated number of accidents happening at the i th Intersection and the ‘q’ intersection parameters, R_i1, R_i2... R_iq, is assumed to be of the same form in the equation:
Log (μ_i) = β₀ + β₁ R_i1 + β₂ R_i2 +……+ β_q R_iq.
Here ‘p_i’ follows a Position distribution with the mean μ_i.
In the negative binomial model the mean value is equal to the variance of the distribution.