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For my master thesis I'm using a binary logistic regression to see whether Brand Type (= dummy) and Attitude towards the advertisement (= continuous) has an effect on the likelihood of people's Willingness to Recommend (DV).

However, my model of fit results are contradicting (see below the results)

The omnibus test indicates a significant result, which would indicate a good fit: χ2 (2) = 29,541, p =<.001)

However, the Hosmer and Lemeshow goodness of fit test is significant, which indicate a poor fit: χ2 (8) = 39,184, p =<.001)

Also the Pseudo R-squares have low values

enter image description here

Than again Wald test indicates that only 1 IV is significant. However, how do you interpret this significance? Because of the contradicting results of the model fit? Do you conclude that the model is not well at predicting (eventhough Brand Type is significant) the outcome variable as most of the results indicate poor results????

enter image description here

The full model: enter image description here

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  • $\begingroup$ These results are not conflicting, but represent different facets of the analysis. To me it seems to be the typical "highly significant, but hardly relevant" issue. Your model summary suggests that the explanatory power of the model is very modest. That a model overall "fits well" does not mean that all its predictors are relevant, only at least one (or combination of some). If you wanted to know whether there is an effect at all, BrandTypeDummy seems to have it. But it is not really informative for the subject's willingness to recommend. $\endgroup$
    – Carsten
    Apr 19, 2020 at 19:45
  • $\begingroup$ Hi Carsten, Thank you for your explanation, that clearifies a lot. However, I have an additional question. My full model implies that no people are willing to recommend, regardless of the brand type or attitude towards the attitude, as shown in the classification table: the sensitivity was 0% and specificity was 100% (Added the model in question) However, the variable BrandTypeDummy is significant as you mentioned as well, which would indicate that people are 2.2 times more likely to recommend boutiques (dummy = 1) compared to high street (dummy = 0). How do you interpret this then? $\endgroup$ Apr 19, 2020 at 20:39
  • $\begingroup$ Why do you use a cut value of 0.5? It seems there are very few "recommenders" and a lot of "non-recommenders". A cutoff at 0.5 would suggest that these are similar in proportion. Note: I am no econometrician, but in my field, ecology, the cutoff is set to the overall prevalence, in your case maybe something like 0.2 or so. That will lead to a different confusion matrix (aka classification table) and you should be able to see the (small) effect of BrandTypeDummy. $\endgroup$
    – Carsten
    Apr 22, 2020 at 14:44

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First, the Hosmer-Lemeshow test is obsolete, as explained at Logistic regression with poor goodness of fit (hosmer lemeshow)?. Then, the two tests are not contradictory, they are about different aspect, as detailed in the comment by @Carsten.

Specifically, the chi-squared omnibus test is not a test of goodness of fit.

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