Logistic regression is often used when the DV is categorical and the IVs are continuous.

I am not sure what you mean by saying "independent variable is measureable" ... however, the kind of regression essentially depends on the nature of your dependent variable: if it is dichotomous (0;1) you should use (simple) logistic regression; if you have a nominal outcome variable (more than two categories) you may consider multinomial logistic regression.

Tobit Regression. 

http://www.ats.ucla.edu/stat/stata/dae/tobit.htm

Dependent variable has only two ordinal outcomes: success or failure –a political candidate may want to know the behaviour of voters, i.e., characteristics of them who may vote for him/her or not. Each voter’s age, profession, etc. have influence on his/her choice to vote for the candidate or not – Binary logistic regression

Dependent variable may have more than two ordianl outcomes: after the high school, student’s selection to “go to university”, “go to vocational training”, “do a job”, or “other” – Multinary logistic regression

Dependent variable is a count: couple’s characteristics affecting their family size. Number of children (0, 1, 2, 3, …): it may have some dependence on their income, ages, etc. – Poisson regression

Dependent variable is period until a particular event happens: time until an employed person finds employment – Cox regression

-VENKAT

I also want to suggest logistic regression

The multinomial logistic regression is ok. If you want to go a step further, I developed a new family of regression models for nominal response. This family extends the multinomial logistic regression to other distributions like normal, Student, Laplace (for symmetric case) and Gumbel or Gompertz (for non symmetric case).

If the nominal dependent variable has two categories Logistic regression should be conducted. If it has more than two categories Multinomial Regression should be done.

Discriminant function , Multiple Discriminant Function and Cluster Analysis

The more general topic are models with "limited dependent variables". They include binary choice models, multi-response models like models for ordered response and multinomial models (e.g., multinomial logit), models for count data like Poisson regression, and Tobit models where the range of the (continuous) dependent variable is censored. See, e.g., Greene, Chapters 21 and 22. 

Use binary logistic regression.

If your outcome is binary (0 and 1) you can use binary logistic regression. If your outcome is multi-nominal you should use the multi-nominal logistic regression, and if your outcome is order you should use the order logistic regression.  

Dear Sevil Hakimi,

you might want to consider in you choice the sample size of your dataset. If the sample is very small i would consider the exact logistic regression rather than the logistic regression which uses the standard maximum-likelihood-based estimator.

the ELR assumes that the log odds of the outcome is modeled as a linear combination of the predictor variables. It is also particularly useful when some of the cells formed by the outcome and categorical predictor variable have no observations.

a better description of your data might help

The type of model useful to be used is based on the DV.

Thus in general the guideline is as follows:

DV                              IV                                      Model

Quantitative        Quantitative/Dummy           MR (multiple regression)

Dummy                Quantitative/Dummy          MBL (multiple binary logistics)

Category              Quantitative/Dummy          MLR                                                                                                                                              (multinominal Logistic Regression)

Note:

All categorical Independent need to be transformed

into dummy variable (for each category).

Good luck

If the outcome (Dependant Variable) is nominal classification (macine learning methods such as decision trees) is a better approach rather than regression.

If you want to use regression methods:

- If there are two dependant values then you can cenvert them to 1 and 0 and try binary logistic regression.

- If there is ordering between dependent values you can convert them to numbers with the same order and try any regression method. 

- If there is no ordering between dependent values then you can produce more than one target attributes (DVs) for each nominal value and combine the results at the end by a metric that you will develop.

There are various considerations at the publications attached such as;

- Missing values

- Nominal values

- Normalisation

as well.

Best wishes.

Article Instance-Based Regression by Partitioning Feature Projections

Article An overview of regression techniques for knowledge discovery

Conference Paper Regression by Feature Projections

Yeah Logistic regression is appropriate

Thanx all

I agree Amin answer.

If the dependent variable has two categories use logistic regression, If the dependent variable has more than two categories use multinomial regression

Nominal logistic regression is better than other statistical methods.

However, Optimal LDF developed by me is the best. See my papers or Springer book.

If you have a nominal or an ordinal dependent variable, I think a Factor Analysis will be the right decision.

binary logistic regression.

binary logistic regression is the appropriate method

I concluded the discriminant functions based on variance-covariance matrices were useless for microarrays in addition to common data.

See my the Pre-Print of BCD'18 (IEEE conference paper) from July 10 to 12. The title is "Cancer Gene Analysis of Microarray Data." My conclusion is that we do not use the discriminant functions such as Fisher's LDF, QDF, RDA, and Lasso. The logistic regression is fairly good because it uses the maximum likelihood. My conclusion is new facts in this research.

Logistic regression is appropriate

My dependent variable is labeled into "rarely", "sometimes" and "often" for consumption of fruits and vegetables. Can I use multinomial logistic regression?

You can even use ordered logistic regression.

Thank you Jochen Wilhelm

I have used both multinomial and binary logistic regression successfully in such cases. It depends on the levels (categories) of the dependent variable. The SPSS has both functions and will generate an output. However when the independent variables are mixed as in both nominal and measurable, the odds ratios won;t be generated for the measurables.