Logistic regression - intepretation of results

#1
Hi all,

I have binary data for which 70% involve 1 (yes) and 30% involve 0 (no). I've done logistic regression in MedCalc. Results below:

Sample size 60
Positive cases a 42 (70,00%)
Negative cases b 18 (30,00%)
a Bacteria = 1
b Bacteria = 0
Overall Model Fit
Null model -2 Log Likelihood 73,304
Full model -2 Log Likelihood 0,0000000536
Chi-squared 73,304
DF 1
Significance level P < 0,0001
Cox & Snell R2 0,7053
Nagelkerke R2 1,0000
Coefficients and Standard Errors
Variable Coefficient Std. Error Wald P
Number -38,25476 12213,08792 0,000009811 0,9975
Constant 1625,82574 519083,33787 0,000009810 0,9975

Could anyone explain why there is so small chi-square p-value and what does it mean, and also the Wald(0,000009811) an P (0,9975).

Those results show low probability which is puzzling because proportion 70/30 is not that big. Am I doing something wrong here?

I would appreciate for any help,

Thanks,

Agata
 

hlsmith

Omega Contributor
#2
Is "Number" a continuous predictor variable? If so, for every 1 unit increase the odds of the outcome are 2.4E-17 times lower, which given your large standard error are not significant (p-value: 0.9975).
 
#3
I am not sure I understand. The "Number" is just a sample "name"/"number". The data looks like this:
1,1
2,0
3,1
4,0
...
50,1
 

noetsi

Fortran must die
#5
I am confused about the variable number as well. How many distinct levels does it have? If it has only a few (like gender) than you should use dummy variables. It has say a hundred possible levels or more (like say temperature) doing it the way you have is fine. I am not sure from the post above how many different levels it has (number is not a good descriptor for a variable btw, you want to call it something that shows what it consist of like temperature, growth, or whatever). Also p values should be .975 not ,975 it is going to confuse people when they see it.

What the result is showing is that this variable has limited impact on the dependent variable. There is no way to know why this is so with statistics, you would have to come up with your own theory of why the impact is limited. The scale of the predictor, what 1 unit means in practice will change the slope. I don't think the scale will change the p value, however, and thus change the results of the statistical test.

You should look at the odds ratio in general for logistic regression. That will not however, change the test of significance. You may not have enough cases to detect significance which can usually be solved by more data.
 

hlsmith

Omega Contributor
#6
It this an empty model, your only predictor is actually just your observation number? In that case number wouldn't have an interpretation unless you sorted your data by outcome (e.g., 0,....,0,1,....,1). What is the purpose on your model?