RES 720 Week 5 Logistic Regression Example

Who Leaves in the First 90 Days? Logistic Regression for a Yes-or-No Outcome

[Student Name]

University of Phoenix

RES/720: Statistical Research Methods and Design II

Week 5 Assignment

[Instructor Name]

[Date]

The learner, the company, its associates and all data are composites written for a model paper.

Early turnover is the problem that started the composite Louisville logistics company's study: 34 percent of new associates leave within 90 days, costing about $4.1 million a year. RQ4 asks which factors predict that outcome. Because quitting within 90 days is yes or no, the regression methods of Week 4 do not fit, and logistic regression is used instead.

Why Logistic Regression

Linear regression applied to a 0-or-1 outcome can predict values below 0 or above 1 and produces residuals that are neither normal nor of equal variance. Peng et al. (2002) explain that logistic regression instead models the natural log of the odds of the outcome as a linear function of predictors, keeping predicted probabilities between 0 and 1, and they recommend reporting coefficients with standard errors, odds ratios with confidence intervals, overall model tests and measures of predictive accuracy.

Data and Predictors

Every one of the 3,600 hires from the two-year window is included: 1,220 quit within 90 days and 2,380 stayed. Predictors match Week 4's: pay, commute, experience, age, shift dummies with fixed days as reference and warehouse dummies, 14 terms in all.

Peduzzi et al. (1996) found in simulations that logistic regression estimates grew biased and erratic when each predictor term had fewer than roughly ten outcome events behind it. With 1,220 quits and 14 terms, this study has about 87 events per term, well beyond that level.

Model Fit

The model with all predictors fit significantly better than an intercept-only model, likelihood ratio chi-square(14) = 212.4, p < .001. Nagelkerke's pseudo R squared was .08; pseudo R squared values in logistic regression run lower than R squared in linear models and are not directly comparable, so the learner reports it without leaning on it.

Odds Ratios

Rotating versus days: OR = 1.72, 95% CI [1.42, 2.08], p < .001.

Nights versus days: OR = 1.21, 95% CI [0.99, 1.48], p = .06.

Commute, per 10 miles: OR = 1.18, 95% CI [1.09, 1.28], p < .001.

Pay, per dollar: OR = 0.89, 95% CI [0.84, 0.94], p < .001.

Experience, per 12 months: OR = 0.93, 95% CI [0.89, 0.97], p = .001.

Age, per 10 years: OR = 0.97, 95% CI [0.90, 1.05], p = .44.

Holding other predictors constant, rotating associates have 72 percent higher odds of quitting than day associates. Each 10 miles of commute raises the odds by 18 percent, and each dollar of hourly pay lowers them by 11 percent.

From Odds to Probabilities

Because a third of associates quit, odds and probabilities differ considerably, and an odds ratio of 1.72 does not mean a 72 percent higher chance. Predicted probabilities make the results usable. For an associate earning $18 an hour with no prior experience at the largest warehouse:

Fixed days, 10-mile commute: 27 percent chance of quitting within 90 days.

Rotating, 10-mile commute: 39 percent.

Rotating, 30-mile commute: 47 percent.

Rotating, 30-mile commute, $20 an hour: 41 percent.

A rotating-shift associate with a long commute is nearly a coin flip to leave within three months.

How Well Does the Model Predict?

Hosmer et al. (2013) caution that overall classification rates can mislead and recommend assessing discrimination with the area under the ROC curve and calibration by comparing predicted and observed rates across groups. At a 0.5 cutoff, the model classified 68 percent correctly, barely better than the 66 percent achieved by predicting that no one quits. The area under the ROC curve was 0.64, modest discrimination. A calibration plot by tenths of predicted risk showed predicted and observed quit rates within 3 points in every group, so the probabilities are trustworthy on average even though the model cannot pick out individual quitters well.

The Onboarding Program and Quitting

In the rollout data from Week 3, 37 percent of associates under the old onboarding quit within 90 days, compared with 29 percent under the new program. A logistic model with the same predictors plus program and rollout period gave an odds ratio for the program of 0.70, 95% CI [0.54, 0.91], p = .007: the program lowered the odds of early quitting by about 30 percent. An interaction between program and shift was not significant for quitting, p = .38, unlike the productivity result, so the program appears to help retention across shifts.

Checking the Model

Variance inflation factors matched Week 4's, all below 3.2. The relationship between commute and the log odds of quitting was checked by adding a squared term and by grouping commute into bands; neither improved fit, so the linear term is retained. Influence diagnostics flagged no single associate whose removal changed any odds ratio by more than 4 percent. Because associates are grouped in nine warehouses, the warehouse dummies again absorb site differences rather than relying on cluster-robust errors.

Using the Model Responsibly

A model that identifies associates at higher risk of quitting could be used in two very different ways. Used to target support, such as assigning a buddy or offering a shuttle to high-risk new hires, it helps both the associate and the company. Used to screen out applicants with long commutes, it could exclude people from lower-income neighborhoods far from the warehouses and expose the company to fairness concerns. The learner recommends the first use only and notes that hiring decisions should not rely on predicted quit risk.

Interpreting Commute and Pay

Commute matters even after shift and pay are considered, which suggests that transportation support, such as a shuttle from bus lines, could reduce early quits. The pay result supports raises at the lowest-paid sites, but because pay varies across warehouses that also differ in other ways, the estimate is an association within warehouses, not the guaranteed effect of a raise.

Limits

The model uses only variables in HR records. Reasons for quitting, such as supervisors, schedules changing without notice or competing job offers, are missing, which helps explain the modest discrimination. The outcome treats all quits alike, though someone who leaves in week one may differ from someone who leaves in week twelve; survival analysis in the dissertation could model timing.

Reporting in APA Style

A logistic regression predicting 90-day quitting was significant, chi-square(14) = 212.4, p < .001, Nagelkerke R squared = .08, AUC = .64. Rotating shifts (OR = 1.72, 95% CI [1.42, 2.08]) and longer commutes (OR = 1.18 per 10 miles) were associated with higher odds of quitting, and higher pay (OR = 0.89 per dollar) and experience (OR = 0.93 per year) with lower odds.

Conclusion

Logistic regression identified rotating shifts, long commutes, lower pay and inexperience as markers of early quitting, and the onboarding program lowered the odds of quitting by about 30 percent across shifts. Predicted probabilities turned odds ratios into terms managers can use, while fit statistics showed that the model describes risk across groups better than it predicts individuals. Week 6 turns to categorical data on safety incidents.

References

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). Wiley.

Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology, 49(12), 1373-1379. https://doi.org/10.1016/S0895-4356(96)00236-3

Peng, C.-Y. J., Lee, K. L., & Ingersoll, G. M. (2002). An introduction to logistic regression analysis and reporting. The Journal of Educational Research, 96(1), 3-14. https://doi.org/10.1080/00220670209598786