Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

The relationship between mental rotation and arithmetic: do number line estimation,working memory,or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.     

Spatio-temporal accident analysis for accident prevention in relation to behavioral factors in driving: The case of South Anatolian Motorway

Analyzing the pattern of traffic accidents on road segments can highlight the hazardous locations where the accidents occur frequently and help to determine problematic parts of the roads. The objective of this paper is to utilize accident hotspots to analyze the effect of different measures on the behavioral factors in driving. Every change in the road and its environment affects the choices of the driver and therefore the safety of the road itself. A spatio-temporal analysis of hotspots therefore can highlight the road segments where measures had positive or negative effects on the behavioral factors in driving. In this paper 2175 accidents resulted in injury or death on the South Anatolian Motorway in Turkey for the years between 2006 and 2009 are considered. The network-based kernel density estimation is used as the hotspot detection method and the K-function and the nearest neighbor distance methods are taken into account to check the significance of the hotspots. A chi-square test is performed to find out whether temporal changes on hotspots are significant or not. A comparison of characteristics related driver attributes like age, experience, etc. for accidents in hotspots vs. accidents outside of hotspots is performed to see if the temporal change of hotspots is caused by structural changes on the road. For a better understanding of the effects on the driver characteristics, the accidents are analyzed in five groups based on three different grouping schemes. In the first grouping approach, all accident data are considered. Then the accident data is grouped according to direction of the traffic flow. Lastly, the accident data is classified in terms of the vehicle type. The resultant spatial and temporal changes in the accident patterns are evaluated and changes on the road structure related to behavioral factors in driving are suggested.