Assessing model stability and sensitivity

Onamusi, Oluwasikemi Oluwadamilola (2022) Assessing model stability and sensitivity. Doctoral thesis, Northumbria University.

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Abstract

Statistical inferences from observed studies with error prone measurements are often biased. The bias is a consequence of the deviation of the probability distribution that generates the observed data from that which generates the true unobserved data. For example, in binary data where measurement error is a misclassification problem, an observation with a true value of 0 is observed as 1 or vice versa. Past research in this framework often focuses on the use of a validation study to account for measurement error in the main study. A shortcoming of this approach is a lack of validation data to inform the correction of measurement error in the main study. Another challenge is the non availability of ready to use statistical software in implementation. To overcome some of the challenges of current approach to the analysis of binary data with measurement error, we investigate the performance of the naive logistic regression model, which we refer to as the assumed model, against a modified model. By modified model we mean an extended logistic regression model, where we introduced the probability of measurement error as a modification weight. The modification weight introduced is in the direction of the nondifferential and differential misclassification pattern. Following Cook’s (1986) normal curvature approach, we derive an influence measure for the special cases of when the presence of binary outcome Y∗i = 1 is error prone, and also for the absence of the outcome Y∗i = 0. The method is applied to a dataset from the rehabilitation programme study for juvenile offenders, where Y∗i = 0 is measured with error. As different compositions of measured values of binary outcomes often exist in real studies, hence, we further conducted a simulation study for different scenarios for the special cases Y∗i = 1 and Y∗i = 0. Our theoretical results show that when there is no information about the error size, the assumed model appears to be the most stable model compared to the modified models. But, the assumed model estimates could be biased when measurement error is present. Thus, it is important to investigate model stability and how model estimates behave within a plausible range of error size, and report all the findings.

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