Hypothesis for logistic regression

#1
I get a group of data and would like to use the regression to analysis the relationship. The dependent variable Y is a kind of loss rate, so it is strictly belong to [0, 1], e.g. I have $100, and I will loss 5% at day 1, 3% on day 2, 4% day 3, ...then Y is (5%, 3%, 4%, ....); I also have some independent variables X1, X2, etc.

Cause Y is belong to [0, 1], when I try the linear regression, I get a lot of negative predicted value when doing the forecast, so I would like to try the logistic regression.

The problem I meet is that, is there any hypothesis for using logistic regression? I choose the family as binomial, the model result is what I would like to see, but I remember that binomial is for 0, 1(classified) problem, can I model the loss rate this way here? Do I need to do any hypothesis test?

Thanks for the kindly help.
 

hlsmith

Not a robit
#2
Rates can be modelled with Poisson. Though your DV is still unclear to me. Is it just those 3 values or anything between 0-1?

Depending on the values of DV I believe in some instances you can log transform it to get a broader scale to work with.

Side note as you noted, logistic is usually used with binary or multinomial data, which it seemed you don't have.
 
#3
Hi hlsmith,

Not only 3 DV, I have about 50 values, by using Poisson as the family, do I need to do any hypothesis test for this? e.g. test the distribution of DV to check if it is possion or not.

For the log transform, I try the transform Z=log(1-Y) and then use the linear regression Z~X1+X2 ..., the problem is on the forecast, I still get negative forecasted loss rate, it is because the independent variable used for the forecast is under stressed.

e.g. I model loss rate ~ GDP + unemployment; for the forecast we use forecasted GDP and umemployment with very strong stressed (with a very large jump), this result in a negative projected loss rate, and it doesn't make sense, so I am thinking to use logistic regression to make sure the forecast loss rate is between 0-1.


I get a group of data and would like to use the regression to analysis the relationship. The dependent variable Y is a kind of loss rate, so it is strictly belong to [0, 1], e.g. I have $100, and I will loss 5% at day 1, 3% on day 2, 4% day 3, ...then Y is (5%, 3%, 4%, ....); I also have some independent variables X1, X2, etc.

Cause Y is belong to [0, 1], when I try the linear regression, I get a lot of negative predicted value when doing the forecast, so I would like to try the logistic regression.

The problem I meet is that, is there any hypothesis for using logistic regression? I choose the family as binomial, the model result is what I would like to see, but I remember that binomial is for 0, 1(classified) problem, can I model the loss rate this way here? Do I need to do any hypothesis test?

Thanks for the kindly help.
 
#4
You do not seem to have a count model here with a transformed DV. As such, neither Poisson nor NegBin models are appropriate. Instead, if your DV is bounded between 0 and 1 check (A) beta regression, and (B) GLM fractional logit -- these would be appropriate for rates and proportions bounded within 0-1. Note though, one model is inclusive of min and max values, whereas the other one is not.