Two goodness‐of‐fit tests for logistic regression models with continuous covariates

Abstract

Assessing goodness-of-fit in logistic regression models can be problematic, in that commonly used deviance or Pearson chi-square statistics do not have approximate chi-square distributions, under the null hypothesis of no lack of fit, when continuous covariates are modelled. We present two easy to implement test statistics similar to the deviance and Pearson chi-square tests that are appropriate when continuous covariates are present. The methodology uses an approach similar to that incorporated by the Hosmer and Lemeshow goodness-of-fit test in that observations are classified into distinct groups according to fitted probabilities, allowing sufficient cell sizes for chi-square testing. The major difference is that the proposed tests perform this grouping within the cross-classification of all categorical covariates in the model and, in some situations, allow for a more powerful assessment of where model predicted and observed counts may differ. A variety of simulations are performed comparing the proposed tests to the Hosmer-Lemeshow test.

Goodness‐of‐fit tests for ordinal response regression models

“…The simulations are similar to that discussed by Pulkstenis and Robinson [4] when evaluating the performance of the proposed tests in the binary logistic regression setting. Data were generated from several cumulative logit models and then models were ÿt which purposely excluded important terms or deviated from the true model in some way.…”

“…The approach generalizes the methodology proposed in the binary logistic regression setting by Pulkstenis and Robinson [4]. Speciÿcally, we propose a two-level subgrouping within each covariate pattern of …”

A Clinical Model To Estimate the Pretest Probability of Lung Cancer in Patients With Solitary Pulmonary Nodules

“…8,9 We used the final model to calculate the estimated probability of malignancy in each study participant. We then compared the predicted probability of malignancy with the final diagnosis and constructed a ROC curve.…”

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“…The exceptions are that the two hybrid statistics N m and N R have p-values less than 0.01. Pulkstenis and Robinson [16] note that their hybrid statistics, although distinct from the hybrid statistics presented here, are not recommended for use in OLR when only continuous variables are in the model. We also note an in ated type I error rate for N R , particularly for model 17 which contains six continuous covariates as in …”

“…Using a similar idea to Pulkstenis and Robinson [16] in OLR, we develop hybrid statistics which combine the ideas of covariate partitioning and using groups based on ranked estimated probabilities. However, our approach di ers from Pulkstenis and Robinson in that we utilize score statistics whereas Pulkstenis and Robinson use deviance and chi-square statistics.…”