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 Pi follows a normal distribution with Mean μi and variance G2. In other words, it is understood that Pi 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 ith intersection and the ‘q’ predictor variables R1,...,Rq, can be given as:
Log (ui) = β0 + β1 Ri1 + β2 Ri2 +……+ βq Riq;
And in the multiplication form it can be written as:
ui = exp (β0) exp (β1 Ri1) exp (β2 Ri1)…… exp (βq Riq);
Where, log is the normal distribution with mean μi 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, Ri1, Ri2... Riq, is assumed to be of the same form in the equation:
Log (μi) = β0 + β1 Ri1 + β2 Ri2 +……+ βq Riq.
Here ‘pi’ follows a Position distribution with the mean μi.
In the negative binomial model the mean value is equal to the variance of the distribution.