My understanding is that the correlation betweeen B0 and B1 has no substantive meaning. It is a scaling artifact that changes based on where the predictor values are centered. The correlation of estimates is needed to create confidence intervals for predicted values - see Fleiss, Levin and Paik (2003) Statistical Methods for Rates and proportions, page 295. For your interest, you should try adding or subtracting a constant and see how it influences the correlation of estimates.

Daniela what is the need to estimate the correlation between the beta of a variable and of an intercept?

Unless I misunderstand your question, this doesnt make sense to do what you are doing...you only have 1 representative value from the equation...it's not like a set of data with multiple observations.

Are you dealing continuous or multi-level discrete independent/predictor variables? Regardless all I am concerned about the Exp(B) value (which is the adjusted odds ratio) and the 95% CI for the Exp(B). Also which form of logistic regression entry of the variables are you using? Forward? Backward?

I agree with Stephen and Audil. The question does not make sense.

Why should you be calculating a correlation between coefficients in logistic regression?

If what you mean is if there is any problem if you get negative coefficients in logistic regression, the answer is no. No problem.

But in this case you shouldn't be talking about "correlation" or "correlation with the intercept".

If you carried out a logistic regression and you got the regression coefficients for the independent variables and for the intercept, you might end up with negative coefficients. This only means that in the model you generated, the variables with negative coefficients are inversely associated to the outcome.

I think Scott Bruce is correct. What matters in logistic regression is the Exp(B) coefficient as well as the level of significance which determined by the wald statistic. It is only when the variable is significant that you will be concerned about it's sign identity.

think Scott Bruce is correct. What matters in logistic regression is the Exp(B) coefficient as well as the level of significance which is determined by the wald statistic. It is only when the variable is significant that you will be concerned about it's sign identity.

Dear Daniela, in the first I would point out that -0.57 does not reflect a really high negative correlation. The value could be rather categorized as medium. Second, I agree with the other contributors that this correlation usually is not performed. Notwithstanding, it provides some information in a way. The intercept does not represent a specific effect, nor can it be interpreted directly. Disregarding mathematical rigor, the intercept reflects all kinds of model shortcomings and misspecifications (omission of variables, measurement errors). It tends to be high and significant in small-scale models with low explicative power. In doing the correlation, you showed that the inclusion of parameter in question is relevant in terms of intercept sensitivity. However, as has already been underlined, such analyses are not common and I do not recommend to include these analyses in your final findings report.

In short if beta coeficient is -0.57 (OR= EXP(-0.57)= 0.5655), it means the evemt will be (1-0.5655) 0.4345 times less likely to occur compared to the reference group.

My understanding is that the correlation betweeen B0 and B1 has no substantive meaning. It is a scaling artifact that changes based on where the predictor values are centered. The correlation of estimates is needed to create confidence intervals for predicted values - see Fleiss, Levin and Paik (2003) Statistical Methods for Rates and proportions, page 295. For your interest, you should try adding or subtracting a constant and see how it influences the correlation of estimates.

The correlations between regression coefficients (in linear regression and logistic regression) are a function of the configuration of the independent variable(s), not the response variable. As Karl Hanson pointed out, if you transform the independent variable (e.g. using X-50 or 50-X instead of X), it may change the sign of the correlation coefficient between the regression coefficients without changing the prediction obtained by using the logistic regression model. So, do not worry about the correlation between the constant term and the other regression coefficients. More worrying would be strong (positive or negative) correlations among the other regression coefficients (if you have more than one predictor) because it would point to multicollinearity among the predictors.

Yes, the correlation I was mentioning is between (b) estimates in a logistic correlation with 2 independent continuous variables, and the estimated intercept. All the coefficients are significant. The correlation of -0.5 I mentioned was not the exp (b), but the correlation between the B of the intercept and the B of one of the variables.

Intuitively I understand that if the intercept is negatively correlated with the slope, the model is a line with bulk of points of high values and some of low value (nonzero), which is my case. To fit a line the slope has to decrease if the intercept increases, thus they are negatively correlated. My concern was that if that is the case, the model estimates (betas) depend too much on each other.

The two independent variables do not start from zero, so Karl’s comment makes a lot of sense.

Thanks a lot,

I might be wrong here, but it seems like you might be using the wrong statistic? If you are concerned about slopes and intercepts then would not a linear or multiple regression be more suited for your data than a logistic regression? I am currently doing my dissertation creating prediction models using logistic regression. I used ROC curve analysis to determine cut-points for my continuous and discrete independent variables and then dichotomized the IVs based on the cut points. I then ran the logistic regression with these dichotomized IVs, using a Backward Entry method for the regression. I was most interested in the Exp(B) and their associated 95% CI, and the Negelkerk(sp?) R2 stats. That's my 2 cents for you. I don't if it helps or not.

In logistic regression you get "slope-like" and "intercept-like" parameters--e.g. what you would use to make a linear logit model, which is then put in the exponent--but I don't understand why you are looking at a correlation between the intercept and the other parameters. If some of the slope parameters were correlated, then you might worry about confounding or direct/indirect effects (by no means lethal to the analysis), but I don't see where the intercept parameter fits in...

I agree with Dr. R. Karl Hanson that B0 is an artifact and should not be considered in the evaluation of odds ratios. In linear regression, the coefficient can be standardized to beta. Logistic regression standardizes each OR to the reference. So if the model is fit and the hypothesis test for the attribute is significant, then the OR can be considered. An estimate of how much of the variance of the dependent variable is explained by the model (pseudo R squared) would be helpful in evaluating your covariates.

I am using the log regression to predict change in land use ( yes/no). And yes, I am looking at the ROC, Negelkerke, etc.

Yes, my explanation on slope and intercept was just a simplification to explain what I understand.

I took a look on the estimates correlations just to see what was going on there, but now with all the explanations I see is not a "real" problem.

Thanks,

Dear Jan Böhnke...

I religiously follow your updates and discussions and have learnt a lot from your discussions.... I do agree that estimating such relations is helpful in some kind of analysis and particularly where relations follow an exponential trend... But I suppose that is the case with 'a coefficient of a predictor with a coefficient of another predictor' and rather not with the 'intercept'. Dear Friend, If I am not wrong Daniela has already checked for collinearity and she has already removed the variables causing collinearity problems... so that should not be the case... As far as I think she doesn't need to go for such kind of an analysis.. But yes if she is confused about what @Lorenzo described above... Explanation for that confusion is well stated there...

I hope Daniela will come up with a little more details on the problems she is facing with her analysis..

Thanks

Khaki

Why are you calculating the correlation between beta and intercept? All you need here is Exp(B) and 95% CI for Exp(B). I will like to know your question of interest before going further on this.