Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Parent modeling and child food consumption

Obesity, among both children and adults, is a growing public health epidemic. One area of interest relates to how and why obesity is developing at such a rapid pace among children. Despite a broad consensus about how controlling feeding practices relate to child food consumption and obesity prevalence, much less is known about how non-controlling feeding practices, including modeling, relate to child food consumption. This study investigates how different forms of parent modeling (no modeling, simple modeling, and enthusiastic modeling) and parent adiposity relate to child food consumption, food preferences, and behaviors towards foods. Participants in this experimental study were 65 children (25 boys and 40 girls) aged 3-9 and their parents. Each parent was trained on how to perform their assigned modeling behavior towards a food identified as neutral (not liked, nor disliked) by their child during a pre-session food-rating task. Parents performed their assigned modeling behavior when cued during a ten-minute observation period with their child. Child food consumption (pieces eaten, grams eaten, and calories consumed) was measured and food behaviors (positive comments toward food and food requests) were recorded by event-based coding. After the session, parents self-reported on their height and weight, and children completed a post-session food-rating task. Results indicate that parent modeling (both simple and enthusiastic forms) did not significantly relate to child food consumption, food preferences, or food requests. However, enthusiastic modeling significantly increased the number of positive food comments made by children. Children's food consumption in response to parent modeling did not differ based on parent obesity status. The practical implications of this study are discussed, along with its strengths and limitations, and directions for future research.^