If I am not mistaken, you have not mentioned your dependent variable here. To determine what kind of model you are going to use, it is not the nature of your independent variable to know. Just tell me what is your response (dependent) variable includes in its classification. So that we may discuss further and help you with R after deciding on the model to use

my dependent variable is unordered and has three different categories.

1- if you have indeed no assumption what factor levels will result in an effect on your DV, dummy coding might be your best choice. If you have hypotheses however, you might want to check out Article How to capitalize on a priori contrasts in linear (mixed) mo...

If you still have the income variable data in numerical form it is the best to use it in its numerical form or in as log-transform depending whether the natural distribution is normally distributed.

2- Removing an entire variable (job) from the equation might dramatically alter your Goodness of fit measure, which should be your best indicator for the, em yes, the goodness of your model. Check the goodness of fit for the model with and without job, it is very reasoinable that not every predictor (job1,2, etc.) influences the DV but taken together they explain the variance in your DV

3- depends on whether you are working as scientist and thus your ultimate goal is to want to find out what is going on or try to maximize the benefit of a model for future use. In the former case you do not split the data to have a maximum cases to draw your conclusions from and in the latter case you would split the data to test your model under conditions that are not the same as under which the model was constructed.

4-see 2

It is always wise to check model assumptions, else your model is not very informative

Concerning 2 and 4, instead of goodness of fit alone you ahould also check information criteria (AIC, BIC ...) because they include the number of predictors in relation to the goodness of fit.

Sven Greving Dear Sven, thanks a lot for your answers,

1- I tried to convert all the categorized variables to dummies with model.matrix function.should i also use the factor function to define the levels before dummies? my income is like1,2,3,.. so on to categorized 0-999 ,999-1999 and so on ,i also put dummies for income;

2- i used library(lmtest) for goodness of fit to consider variables like job,should iconsider p value only ?i mean how should i compare models toghether?

3- i want to predict number of cars per household,how should i define assumption for my model?

thank you in advance for your time

Is your DV the number of cars? Why would you use this as categorical variable.

For comparison of mlogits check out http://utstat.toronto.edu/~brunner/oldclass/312f12/lectures/MultinomialLogitWithR.pdf

because in my data set household has 0,1,2,...,10 cars,for me it is important to know 1,2 3 or more,i mean the exact number is not important just want to know one ,two ,three or more,,they are three categories ,

sorry i was completely wrong,i was thinking about orderd,unorderd models,i mean my DV is unordered,that is why i want yo use MNL model