I am performing statistical analysis on a data where I am trying to see observe the impact of factors like sex, area of residence and literacy on outcome variables.
I don't have any SPSS subscription and I can't find the budget to obtain one at this time. So, I am using Jamovi. I also downloaded the trial version to SPSS. I ran multinomial logistic regression analysis with both Jamovi and SPSS and I noticed the following:
- The results are identical but...
- Cox-Snell Pseudo R-squared value and Nagelkerke Pseudo R-squared value are quite different between Jamovi and SPSS while McFadden's Pseudo R-squared value is identical.
- SPSS also reports Wald Statistic while Jamovi doesn't.
So, is it important to report Wald Statistic when reporting multinomial logistic regression results in a paper? I see that many papers do report the Wald Statistic, but I want to finish the full analysis using Jamovi and I can't get Wald value with that.
It should be noted that I don't have much experience in the field of statistics in general.
The Wald statistic is derived from the ratio of the estimate (b) to the standard deviation: b/se and asymptotically has a standard normal z distribution. So it is an approximate statistic and for logistic regression usually a worse choice than using the likelihood chi-square (the change in deviance between models with and without the tested predictors). You can also can derive an approximate chi-square statistic from the Wald statistic because a sum of k squared z distributions is a chi-square distribution with k df. So for a single predictor the Wald z statistic z^2 = X^2(1). This chi-square statistic isn't the same as the likelihood chi-square or indeed the Pearson chi-square that programs like SPSS report. If you have the likelihood chi-square statistic that's generally considered a better option than Wald statistics - though asymptotically they should be identical (so it may not matter in sufficiently large samples).
In summary - not having Wald statistics (which are approximate) is not necessarily a problem. Also if you have b and SE (which any software should report) then you can calculate the Wald statistic with relative ease.
Dearly respected, the Wald in SPSS is the Chi-Square for each variable, I don't know the other system you have used. I suggest using one of the two Packages. If you choose the SPSS, then Wald is quite important.
Once you are reporting the odds ratio with 95% CI, reporting other statistics is not important. Even reporting p-values have less value in this case.
Agreed, however, the odds ratio for what? for the non-biostatistician reader?
The P-value, the dichotomization, and the Null hypothesis are excellent reminders from you Md. Belal Hussain.
Thanks, Hyder Mirghani. My point is that interpreting the results in plain language is my responsibility as a researcher. The odds ratio is very intuitive. For example, an odds ratio of 1.6 can be interpreted as 60% more likely to have the disease among exposed compared to unexposed. I think anyone can understand this.
Interpretation based on p-value is should be avoided as calculation of p-value depends on the sample size. For example, how could we interpret the odds ratio of 1.6 with a p-value of 0.06 (say, 95% CI: 0.9-2.1)? There is no association? This is incorrect. Because it's clear from the odds ratio that the exposed are 60% more likely to experience the outcome. Here is an excellent discussion on it: https://link.springer.com/article/10.1007/s10654-016-0149-3
Dichotomising of a continuous variable has many consequences (loss of information, statistical power issue, underestimation of variance, etc.). Hypothesis (or null hypothesis) is the key to our study. I am not sure what do you mean by excellent reminders.
The Wald statistic is derived from the ratio of the estimate (b) to the standard deviation: b/se and asymptotically has a standard normal z distribution. So it is an approximate statistic and for logistic regression usually a worse choice than using the likelihood chi-square (the change in deviance between models with and without the tested predictors). You can also can derive an approximate chi-square statistic from the Wald statistic because a sum of k squared z distributions is a chi-square distribution with k df. So for a single predictor the Wald z statistic z^2 = X^2(1). This chi-square statistic isn't the same as the likelihood chi-square or indeed the Pearson chi-square that programs like SPSS report. If you have the likelihood chi-square statistic that's generally considered a better option than Wald statistics - though asymptotically they should be identical (so it may not matter in sufficiently large samples).
In summary - not having Wald statistics (which are approximate) is not necessarily a problem. Also if you have b and SE (which any software should report) then you can calculate the Wald statistic with relative ease.
I have a different take on the Wald statistic. Based on my student's and my work on the applications of robust logistic regression we find the Wald statistic to be the foundation for robust testing in these models. In particular the paper that developed these robust tests (file:///C:/Users/user/AppData/Local/Temp/BiancoRobust7-2.pdf) powered our work in this area, e.g. our papers can be downloaded at this link: https://scholar.google.com/scholar?hl=en&as_sdt=0%2C36&q=Robust++logistic+regession+hauser+Booth&btnG=
Further the first algorithm to do robust logistic regression was developed by Bianco and Yohai, A classic in robust regression. (see the above links for the cite). The current algorithm cited in the above papers is based on the work of Bianco and Yohai. Further in all the logistic regression programs that I am familiar with the Wald static is used for the tests on individual regression coefficients. Based on these results (which I admit are asymptotic distributions) we have found this work to be quite useful. BTW I am not being critical of the above replies, simply looking from, I believe, a different point of view. Best wishes to all, D. Booth BTW should one prefer the Chi-square approach, I believe the needed results are all in the Bianco and Martinez paper cited above
Thanks to all who responded to this question. I guess the next thing that comes to my mind is:
What information does a Wald Statistic value convey? I know what odds ratio conveys, or what p value conveys. But I don't understand what is indicated by a Wald Statistic value of say 2.3114.
Of course, again, I don't have much experience on this logistic regression modeling at all.
Shadid Uz Zaman You might look at the papers cited in my above reply and the attached. Best wishes, David Booth
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