East Carolina University



Binary Logistic Regression: Predicting Metabolic DiseaseRead this article to get a feel for what the variables are. Here I use these data to illustrate how to interpret the output from a simple binary logistic regression. The analysis reported in the article is more complex. My students can find the article in BlackBoard, Articles, Multiple Correlation/Regression, Binary Logistic with Multiple Imputation.Aziz, S., Wuensch, K. L., & Shaikh, S. R.? (2017).? Exploring the link between work and health: Workaholism and family history of metabolic diseases.??International Journal of Workplace Health Management,?10, 153-163.?? doi: 10.1108/IJWHM-05-2016-0034The OutputCase Processing SummaryUnweighted CasesaNPercentSelected CasesIncluded in Analysis259100.0Missing Cases0.0Total259100.0Unselected Cases0.0Total259100.0a. If weight is in effect, see classification table for the total number of cases.Dependent Variable EncodingOriginal ValueInternal ValueNone0Some1The outcome variable was whether or not the subject had a personal history of metabolic disease.Block 0: Beginning BlockClassification Tablea,bObservedPredictedAny Self IllnessPercentage CorrectNoneSomeStep 0Any Self IllnessNone1640100.0Some950.0Overall Percentage63.3a. Constant is included in the model.b. The cut value is .500Just knowing the base rate of having metabolic illness enables us correctly to predict the outcome 63.3% of the time. Since most respondents had not (yet) had a metabolic disease, the prediction was, for every case, that the individual did not have metabolic disease. The percentage of correct classifications equals the percentages of subjects who did not have metabolic disease, 164/259 = 63.3%.Variables in the EquationBS.E.WalddfSig.Exp(B)Step 0Constant-.546.12917.9321.000.579The null tested here is that half of the cases have had a history of metabolic illness and half have not. The odds ratio is the ratio of the number who have had such a history to the number who have not, which equals 95/164 = .579.Variables not in the EquationScoredfSig.Step 0VariablesAny Family Illness6.6501.010Zscore: How old are you (in years)?19.0341.000Zscore(WART_Total)4.3401.037Zscore: Hours of Exercise per Week10.3991.001Overall Statistics39.8644.000The table above tests the null that adding one of the predictors available to the intercept-only model would not improve the fit between model and data. As you can see, adding any of these predictors would significantly improve the fit between model and data.Block 1: Method = EnterOmnibus Tests of Model CoefficientsChi-squaredfSig.Step 1Step44.5384.000Block44.5384.000Model44.5384.000Adding those four predictors significantly improved the fit between model and data.Model SummaryStep-2 Log likelihoodCox & Snell R SquareNagelkerke R Square1295.906a.158.216a. Estimation terminated at iteration number 5 because parameter estimates changed by less than .001.Classification TableaObservedPredictedAny Self IllnessPercentage CorrectNoneSomeStep 1Any Self IllnessNone1362882.9Some464951.6Overall Percentage71.4a. The cut value is .500Now we can correctly predict 71.4% of the cases. The intercept-only model correctly predicted 63.3%. With having metabolic disease being the target event, and a .5 cutoff, sensitivity was 51.6% and specificity 82.9 percent.Variables in the EquationBS.E.WalddfSig.Exp(B)Step 1aAny Family Illness1.130.4975.1691.0233.095Zscore: How old are you (in years)?.671.15618.6401.0001.957Zscore(WART_Total).320.1434.9861.0261.377Zscore: Hours of Exercise per Week-.552.17310.1561.001.576Constant-1.661.47712.1311.000.190a. Variable(s) entered on step 1: Any Family Illness, Zscore: How old are you (in years)?, Zscore(WART_Total), Zscore: Hours of Exercise per Week.Each one of the predictors had a significant unique effect.Subjects with a family history of metabolic disease were 3.095 times more likely to have a metabolic disease than were those with no such family history.Each one standard deviation increase in age nearly doubled (1.957) the odds of having a metabolic disease Each one standard deviation increase in workaholism multiplied the odds of having a metabolic disease by 1.377.Inverting the odds ratio (1/.576 = 1.736), each one standard deviation increase in amount of exercise multiplied the odds of no having a metabolic disease by 1.736. ................
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