Specially traffic and transportaion problem include lot of randomness in events so i am looking for adavnatges and disadvantages of modelling approach..I know logit model include random compnent and also probit with different distribution of random component. what is best circutnaces to use it?

Logit and probit models provide similar distributions with a very slight variation at some point. The difference is on their nature of equations used where probit uses a cummulative standard normal distribution function while logit model uses a logarithmic equation. The logit model is preferred to that of probit since probit involves integration of a standard normal distribution function which can be tedious.

Modeling is all about fitting the actual observation or trend to follow a particular pre- defined distribution. Since there is a lot of distribution functions, different models fits in data differently. The goodness of fit can be determined by different methodologies like least square deviations or determination of likelihood ratios.

So choice of any model to use actually will depend on the nature of the problem you are dealing with. Some fits certain models better than others and vice versa.

Thanks

I can say that Linear modeling is not a good tool since very few distributions will follow a linear nature. Since we have the statistical software to do all the tough work for us it is better to use other models that will better explain our data

So least squre deviation or likely hood ratio are only parameters or there could any other parameters Adjusted R-squared, S.E. of regression, Sum squared resid, F-statistic., Akaike info criterion

Schwarz criterion

Hannan-Quinn criter.

Durbin-Watson stat

I am confused with all these parameters. Which one will be best to compare among logit and probit. Another question is what is the Pvalue in modelling. Is it to multiply with coefficient when we want final prediction?

You are right, there exist a lot of parameters, each with its own function, advantages and disadvantages.

For instance, R-square increases with the size of data. So, the more data you have, the higher the R-square.

As another example, t-statistic increases as the standard error decreases in estimating a parameter, and this is useful indeed. The higher the t-statistic, the higher our confidence in that parameter.

So, what is your main concern in modelling, this is the first question to answer.

I am looking for performance evaluation of model -linear, binary logit , probit and mixed logit also. Confused with parameters. How to get it done is there any guidance??

Just adding to Evarist's answer: Be careful about overfitting your data. 

When you say performance evaluation, do you mean comparative performance evaluation? In other words,are you comparing between 2 models, where you have produced the 2nd model by adding or subtracting a variable to the first? 

If you are not making comparative performance evaluation, then R2 is not useful as it simply increases with the size of the data. If you  are  making  comparative evaluation between 2 similar & comparable models, then R2 is useful; this is because an increasing R2 suggests that, by adding or subtracting a variable from your model, you are explaining a greater percentage of the phenomenon you are modelling. 

R2 cannot tell that your model is explaining a phenomenon correctly. It can only suggest that, between 2 comparable models, one model is more explanatory than the other. However, you may still be explaining the phenomenon in the wrong way!

If this is helpful, i could continue with the meaning of t-statistic.

The simple way I can think of explaining is this,

Use of certain model depends on the nature of the data you are using. Each model has its advantages and limitations for each dataset

1. Linear Models(Regression)> Are used when you have metric variables both explanatory and explained. Test for Performance or goodness of fit you use R-squared

2. ANOVA or MANOVA are also applied on the above-mentioned variables but MANOVA is extended to apply when you have some non-metric explanatory variables(But the outcome has to be metric). Test for performance/Goodness of fit you use Chi-square test.

3. Negative Binomial Models, Poisson, Gamma- Are used for models with both metric and non metric explanatory variables but with count outcomes like number of occurences (eg crashes, or arrivals etc)Test for performance here uses log-likelihood test which can also sometimes be presented as chi-square.

4. Logit/ Probit Regression Models for binary or Multinomial. This can be used for any model, kind of explanatory variables but for outcome variable, must be categorical> binary for the Binary models(Means two categories) and  More than two outcomes for multinomial. Test for performance here also uses log-likelihood test which can also be presented as chi-square.

That is to the best of my knowledge.