Influential observation detection in the logistic regression under different link functions: an application to urine calcium oxalate crystals data

This study compares the performance of link functions for diagnostic methods to diagnose influential observations in the logistic regression model. Four link functions, i.e. logit, probit, clog-log and cauchit are considered to identify which link function gives the best results. We used Cook's distance, DIFFITS and CVR as diagnostic methods. We compare the performance of influence diagnostics with the link functions using the simulation study and a real-life application. Results show that the CVR with logit link function is a good method for small explanatory variables. For large explanatory variables and small sample sizes, the performance of the cook's distance and DIFFITS with probit and logit link function is better than the CVR method. Similarly, for large explanatory variables and sample sizes, the cook's distance (with probit and logit link functions) and CVR with cauchit link function give the same performance and are better than the DFFITS method.

Automated summary

This study compares the performance of different link functions in diagnosing influential observations in the logistic regression model. The results show that the CVR method with the logit link function is good for small explanatory variables. For large explanatory variables and small sample sizes, the cook's distance and DIFFITS with probit and logit link functions perform better than the CVR method. Similarly, for large explanatory variables and sample sizes, the cook's distance (with probit and logit link functions) and CVR with cauchit link function have the same performance and are better than the DFFITS method.