Modeling repeated ordinal responses using a family of power transformations: application to neonatal hypothermia data

BACKGROUND: For analyzing a repeated ordinal response, it is common to use a multivariate cumulative logit model. This model may fit poorly, especially when a nonsymmetric response is available. In these cases, alternative strategies should be utilized. METHODS: In this paper, we present a family of power transformations for the cumulative probabilities to model asymmetric departures from the random-intercept cumulative logit model. To illustrate this method, we analyze the data from an epidemiologic study to identify risk factors of hypothermia among newly born infants in some referral university hospitals in Tehran, Iran. RESULTS: For hypothermia data, using this family of transformations and comparing the goodness-of-fit statistics showed that a model with the cumulative complementary log-log link gives us a better fit compared to a model with the cumulative logit link. CONCLUSION: In some areas, using the ordinary cumulative logit link function does not lead to the best fit. So, other link functions should be evaluated to discover the best transformation for the cumulative probabilities.