A smooth test of goodness-of-fit for growth curves and monotonic nonlinear regression models

We propose a goodness-of-fit test for growth curves based on an adaptation of the data-driven smooth test paradigm. It is simple to apply and can assess the fit of a model to a set of growth experiences. A simulation study shows that for small samples, the test holds its level. Moreover, its power is found to be generally greater than existing tests. The article concludes by revisiting the long-standing problem of validating a model for the growth of human stature.     

Testing goodness of fit for stochastic models of carcinogenesis.

This paper considers the utility of statistical goodness of fit testing in the context of mechanistic models of carcinogenesis. Two stochastic models of carcinogenesis were tested with several sets of experimental and epidemiological data using a formal goodness of fit test specially designed to accommodate censored observations: these were the two-stage model allowing for clonal expansion of initiated cells and its simpler version with gamma distributed promotion time. The results of this application, supplemented by visual examination of local likelihood kernel estimates of the hazard function and the corresponding model-based estimates, show that mechanistic models of carcinogenesis provide a good fit to the data in the majority of cases under study.     

Assessing the goodness of fit of logistic regression models in large samples: A modification of the Hosmer-Lemeshow test

Evaluating the goodness of fit of logistic regression models is crucial to ensure the accuracy of the estimated probabilities. Unfortunately, such evaluation is problematic in large samples. Because the power of traditional goodness of fit tests increases with the sample size, practically irrelevant discrepancies between estimated and true probabilities are increasingly likely to cause the rejection of the hypothesis of perfect fit in larger and larger samples. This phenomenon has been widely documented for popular goodness of fit tests, such as the Hosmer-Lemeshow test. To address this limitation, we propose a modification of the Hosmer-Lemeshow approach. By standardizing the noncentrality parameter that characterizes the alternative distribution of the Hosmer-Lemeshow statistic, we introduce a parameter that measures the goodness of fit of a model but does not depend on the sample size. We provide the methodology to estimate this parameter and construct confidence intervals for it. Finally, we propose a formal statistical test to rigorously assess whether the fit of a model, albeit not perfect, is acceptable for practical purposes. The proposed method is compared in a simulation study with a competing modification of the Hosmer-Lemeshow test, based on repeated subsampling. We provide a step-by-step illustration of our method using a model for postneonatal mortality developed in a large cohort of more than 300 000 observations.