Hi Mohsen. From this result it seems that your sample has mostly 0's in the response variable, with very little 1's. Is this the case?

Cheers

Hi Bruno,

That's right!

So how will you argue?

Thanks for the answer.

In that case I would say that the results of the model are rational, as they reflect the results in the sample.

If you think that your model doesn't suit your research needs you can:

1) Increase your sample size in a way that you increase your positive responses (1's) in order to have a more balanced sample,

2) Try models that can deal with the type of sample you have. I recommend you take a look at "Zero Inflated Models and Generalized Linear Mixed Models with R (Zuur , 2012).

Thanks Bruno. I’ll try your recommendations.

Hello Mohsen,

Glad you are getting some input here. I’ll add my 2 cents worth.

Since you have are conducting logistic regression, your regression parameters are on the logit scale – meaning they are pretty uninterpretable when simply looking at them. In a linear regression context, we would say for every 1-unit increase in x, y increases/decreases by “whatever the regression parameter is”. That doesn’t work when you are using a different link function (e.g., logistic regression).

So, you can certainly look at probabilities to bring some meaning to the outcome, but I think your question is how to interpret the magnitude. This is best done by using the odds ratio (OR = e^logit value; your logit value is the regression parameter). The odds ratio is the odds of your outcome=1 given x =1 over the odds the outcome=1 given x=0. So as an example, a logistic regression parameter for x of 1.467 would give you an odds ratio 4.336. Therefore, the odds ratio says you are 4.3 times more likely to have outcome =1 when x=1.

An odds ratio of 1 would mean no effect (and would certainly be non-significant). An odds ratio below zero means “less likely” and the odds ratio is usually more interpretable by calculating 1/OR; this is because the “less likely scale” is bounded by zero. So, for example, a logit value of = -1.217 provides an odds ratio of 0.296, and this would be described as being 3.4 times less likely to … when x=1 (i.e. calculated by 1/.296).

I hope this is helpful Mohsen, and I wish you well in your research!

Tim

Thank you Tim, for your helpful explanation.

Dear Tim, please take a look at this question.

Can I say that since all the variables are binary and have a positive coefficient, a variable with bigger coefficient have bigger impact on the probability derived from Z?

Hello Mohsen,

Generally, yes … all variables being binary. However, I would argue (as you have in your opening question) that you need to transform your (logit) coefficients into probabilities. This helps in discussing and comparing the parameters in a way that the reader can understand. It’s next to impossible to communicate different types of non-linear parameters (like logit, cubic, probit, etc) in a write-up and make sense of them.

So, I think you are on the right track with transforming the regression parameters into probabilities. Keep in mind, that you don’t really have to break them down into all possible groupings. Each transformed parameter, is the increase/decrease in probability for the DV for that independent parameter =1 (assuming your binary variables are 0 or 1), HOLDING all other variables in the equation equal.

However, because these predictors have covariance (as one would expect), the probabilities are not simply additive (e.g., the probability for x & y =1 is not the same as adding up the probabilities of when only x=1 and separately when y=1; in your example at the top).

The odds ratio is a better way of showing the magnitude of for each independent parameter.

I have added a spreadsheet for doing the logit conversions, in case it is helpful.

Wishing you well,