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.     

Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms

Abstract

Direction dependence analysis (DDA) makes use of higher than second moment information of variables (x and y) to detect potential confounding and to probe the causal direction of linear variable relations (i.e., whether x?→?y or y?→?x better approximates the underlying causal mechanism). The “true” predictor is assumed to be a continuous nonnormal exogenous variable. Existing methods compatible with DDA, however, are of limited use when the relation of a focal predictor and an outcome is affected by a moderator. This study presents a conditional direction dependence analysis (CDDA) framework which enables researchers to evaluate the causal direction of conditional regression effects. Monte–Carlo simulations were used to evaluate two different moderation scenarios: Study 1 evaluates the performance of CDDA tests when a moderator affects the strength of the causal effect x?→?y. Study 2 evaluates cases in which the causal direction itself (x?→?y vs y?→?x) depends on moderator values. Study 3 evaluates the robustness of DDA tests in the presence of functional model misspecifications. Results suggest that significance tests compatible with CDDA are suitable in both moderation scenarios, i.e., CDDA allows one to discern regions of a moderator in which the causal direction is uniquely identifiable. An empirical example is provided to illustrate the approach.     

Exploratory regression analysis: A tool for selecting models and determining predictor importance

Linear regression analysis is one of the most important tools in a researcher’s toolbox for creating and testing predictive models. Although linear regression analysis indicates how strongly a set of predictor variables, taken together, will predict a relevant criterion (i.e., the multiple R), the analysis cannot indicate which predictors are the most important. Although there is no definitive or unambiguous method for establishing predictor variable importance, there are several accepted methods. This article reviews those methods for establishing predictor importance and provides a program (in Excel) for implementing them (available for direct download at . The program investigates all 2 ^p – 1 submodels and produces several indices of predictor importance. This exploratory approach to linear regression, similar to other exploratory data analysis techniques, has the potential to yield both theoretical and practical benefits.     

Posttraumatic Growth and HIV: A Study on Associations of Stigma and Social Support

The present study investigated the influence of HIV‐related stigma and social support on posttraumatic growth (PTG) in adults with HIV (N = 126). The study examined if social support moderated the relationship between stigma and PTG. Results from the study revealed that the predictor variables contributed significantly to PTG following an HIV diagnosis; however, no significant interaction effect between the 2 variables was found. Implications for counselors and directions for future research are provided.     

A note on the Neyman-Johnson technique

A statistical problem which frequently arises in educational and psychological experimentation is that of testing the significance of the difference of the mean scores of two groups on some criterion variable, where the differential effects of one or more variables which are correlated with the criterion must be statistically eliminated. The usual analytical technique for this type of problem is the analysis of covariance (9). The Neyman-Johnson technique (7) provides another, and substantially different, approach. A computational procedure is suggested here which utilizes the advantages of both techniques without an undue increase in computational labor. In addition, the Neyman-Johnson technique is generalized to the case ofn predictor variables. Its application has heretofore been limited to a maximum of three predictor variables.This paper was written while the author was a Psychometric Fellow of the Educational Testing Service, Princeton, New Jersey.     

Validity of General Mental Ability for the Prediction of Job Performance and Training Success in Germany: A meta‐analysis1

A meta‐analysis into the operational validity of general mental ability (GMA) measures in Germany is presented. The meta‐analysis addresses the question whether findings of US and European meta‐analyses are generalizable to Germany given the differences in the education systems of these countries. The high level of differentiation in the German educational system is expected to enhance the homogeneity of applicant pools resulting in a low level of variability in predictor scores which reduces the observed GMA–performance relationships. Our analysis is based on 54 independent German articles and unpublished reports. Results indicated an operational validity of ρ=.467 for training success (k=90; N=11,969) and ρ=.534 for job performance (k=9; N=746). Moderator analyses showed that job complexity and the year of publication are relevant moderator variables, with lower job complexity levels and older studies being associated with higher operational validities. Findings suggest that overall German operational validities are comparable with findings in the United States or other European countries. However, for training success operational GMA validities are slightly lower in Germany compared with US or European meta‐analyses.     

Children's Classification Skills as Predictors of Their Referential Communicative Encodings

Younger and older children's classification skills were assessed, and their classificatory performance was used as a predictor variable in a multiple-linear-regression analysis to determine whether their classificatory skills accounted for a significant proportion of the variance in their performance on referential communication tasks. We tested 10 boys and 10 girls at each of six age levels between 5 and 10 years individually on a vocabulary test, four classification tasks, and six referential communication tasks. Order of task presentations was counterbalanced; reliabilities for all tasks were high. A series of related multiple-regression analyses showed that grade and vocabulary accounted for a significant proportion of the variance on the referential communication tasks; the series also showed a large decrease in the F value for grade and vocabulary when the contribution of the classification variables was partialled out. No evidence for an independent contribution of the classification variables was found.     

Simple and multiple P‐splines regression with shape constraints

In many research areas, especially within social and behavioural sciences, the relationship between predictor and criterion variables is often assumed to have a particular shape, such as monotone, single‐peaked or U‐shaped. Such assumptions can be transformed into (local or global) constraints on the sign of the nth‐order derivative of the functional form. To check for such assumptions, we present a non‐parametric regression method, P‐splines regression, with additional asymmetric discrete penalties enforcing the constraints. We show that the corresponding loss function is convex and present a Newton–Raphson algorithm to optimize. Constrained P‐splines are illustrated with an application on monotonicity‐constrained regression with both one and two predictor variables, using data from research on the cognitive development of children.     

Is it enough to be willing to win or do you have to be smart? The relationship between competitive worldviews,cognitive abilities,and applicant faking in personality tests

Recent research has highlighted competitive worldviews as a key predictor of faking—the intentional distortion of answers by candidates in the selection context. According to theoretical assumptions, applicants’ abilities, and especially their cognitive abilities, should influence whether faking motivation, triggered by competitive worldviews, can be turned into successful faking behavior. Therefore, we examined the influence of competitive worldviews on faking in personality tests and investigated a possible moderation of this relationship by cognitive abilities in three independent high school and university student samples (N₁ = 133, N₂ = 137, N₃ = 268). Our data showed neither an influence of the two variables nor of their interaction on faking behavior. We discuss possible reasons for these findings and give suggestions for further research.     

Optimism as a mediator between resilience and affective states in older adults / El optimismo como mediador entre la resiliencia y estados afectivos en adultos mayores

Abstract

The purpose of this study was to explore whether resilience is associated with and a predictor of depression, anxiety, negative and positive affect, life satisfaction and subjective happiness in older adults, and whether these relationships are mediated by optimism. To analyse this, different scales were administered to a sample of 240 elderly people and correlational and mediational analysis was carried out. The results showed relationships between all the variables. Similarly, we found that optimism is a partial mediator of the relationship between resilience and the aforementioned variables. Our results evidenced that increasing resilience and optimism in elderly people could be favourable to successful ageing.     

Investigating the nature of expressiveness in stranger,acquaintance and intrafamilial homicides

This study explores the role of the victim–offender relationship in the dynamics of homicide, by examining the crime scene behaviour of 25 intrafamilial, 30 acquaintance and 27 stranger homicide offenders (n = 82). Six crime scene variables were examined: ‘Weapon from the scene’, ‘Excessive wounding’, ‘Facial trauma’, ‘Multiple wounds to a single area’, ‘Post‐mortem activity’ and ‘Manual violence’. The first objective was to identify whether these variables could be combined to form a partially ordered scale of expressiveness. The second was to examine whether the nature of this expressive crime scene varied according to the victim and offender relationship. It was hypothesised that the intrafamilial homicides would be characterised by a more expressive crime scene. This was examined by Partial Order Scalogram Analysis which supported the hypothesised link between the level of expressed emotion evident in the crime scene and the nature of the victim–offender relationship. Further analysis on the individual variables revealed that the best single predictor of the relationship between victim and offender was the presence of multiple wounding. These findings are discussed both as contributing to a theoretical understanding of the emotional salience of crime scene actions when killing a family member, and in practical terms in relation to the significance of these variables for both police investigations and clinical interventions with homicide perpetrators. Copyright © 2005 John Wiley & Sons, Ltd.     

Personality factors as predictors of pathological gambling

The aim of this study was to investigate the relationship between different personality variables and pathological gambling (PG). The NEO-FFI and measures of impulsivity and sensation-seeking were administered to a sample of pathological gamblers (n = 90) and to a contrast group of non-pathological gamblers (n = 66) matched on sex and age. Gender, age, education level and the personality variables were entered into crude and adjusted logistic regression analyses with PG-status as the dependent variable. The results showed that educational level and all personality variables were significant predictors of PG in the crude analyses, however only four of the 12 significant predictor variables (Neuroticism, Openness, Impulsivity, and need for Stimulus Intensity) remained significant in the adjusted analysis. All predictor variables accounted for 71% of the variance in PG-status. Clinical implications of the findings are discussed.     

The relationships between contact,status and prejudice: An integrated threat theory analysis of Hindu–Muslim relations in India

In the context of Hindu–Muslim relations in India, the present study (N = 87) utilized Integrated Threat Theory (Stephan & Stephan, 2000 ) to examine the mediating roles of intergroup anxiety, realistic and symbolic threats and the moderating role of group membership (Hindu vs. Muslim) in the relationships between cross‐community contact, relative in‐group status and prejudice. Overall, intergroup anxiety and realistic, but not symbolic, threat emerged as proximal predictors of prejudice and partial mediators between the predictor and criterion variables. But these findings were qualified by majority (Hindu) versus minority (Muslim) group membership. As predicted, while symbolic threat was a predictor of prejudice for Hindus, realistic threat was a paramount predictor for Muslims. In‐group status was as a significant predictor for low‐status minority group only. The results are discussed with reference to their potential implications for future research and interventions aimed at improving intergroup relations. Copyright © 2008 John Wiley & Sons, Ltd.     

Role stress reexamined: An investigation of role stress predictors

R. L. Kahn, R. P. Wolfe, R. P. Quinn, J. D. Snock, and R. A. Rosenthal (1964, Organizational Stress: Studies in Role Conflict and Ambiguity, New York: Wiley) distinguished three different types of predictor of role stress; personal, interpersonal, and organizational. Based on a sample of young professional engineers this investigation studied the relationship betwen these three types of predictor and four forms of role stress (role conflict, role ambiguity, quantitative role overload, qualitative role underload). The relationship was studied both within each predictor set and between each predictor set. Employing bivariate and multiple regression analyses, variables were identified within each predictor set which were significantly predictive of role stress. In addition, comparison was made between the sets of predictor variables selected and between each of the four role stresses that were studied. The results support the relevance of personal, interpersonal, and organizational predictors to role stress, as well as suggesting that role stress researchers should pay more attention to differentiating between varying forms of role Stress.     

Predicting intention and behaviour following participation in a theory-based intervention to improve gluten free diet adherence in coeliac disease

Objective: To determine whether changes in theory of planned behaviour (TPB) constructs could predict intention and gluten-free diet (GFD) adherence following participation in an online theory-based intervention designed to improve adherence in coeliac disease.

Design: Theory-based process evaluation of the mechanisms of change over the course of a six-week online intervention. Measures of GFD adherence and TPB variables were administered at baseline and follow-up (immediate post-intervention: n = 74; three-month: n = 68; six-month: n = 65). Hierarchical regression analyses using residualised change scores were conducted at each time point (dependent variables: intention and adherence).

Results: Baseline intention and GFD adherence were the strongest predictors of follow-up intention and adherence, respectively. Change in attitude accounted for significant variance in intention. Change in intention accounted for significant variance in GFD adherence immediately post-intervention; by the six-month follow-up change in perceived behavioural control was the stronger predictor.

Conclusions: Partial support for the hypotheses suggests that, for certain behaviours, the TPB may be relevant in explaining the mechanism of action responsible for changes in intention and behaviour following participation in a behaviour change intervention. Additional predictive pathways are also likely to exist and, in the area of GFD adherence, may include habit strength and actual behavioural control.     

The Appreciation of Humor in Captioned Cartoons

Humor appreciation for captioned cartoons was studied as a function of cartoon category and eight predictor variables: complexity, difficulty, fit, depth, visual humor, artwork, vulgarity, and originality. Preference and funniness proved to be virtually identical as criterion variables and were combined as appreciation for further analysis. A nonmetric factor analysis of appreciation ratings yielded four dimensions: (a) Sexual, (b) Incongruity, (c) Social Issues, and (d) Marriage-Family. Sexual and Marriage-Family were the most appreciated categories, Social Issues the least appreciated. Fit and originality were the only predictor variables with significant relationships to appreciation independent of the category effect. Cartoons judged to have the most originality and the best fit between drawing and caption were most appreciated. The results suggest that the kinds of cognitive processes involved in cartoon-humor appreciation are very similar to those involved in environmental preference.     

Identifying gender differences in the independent effects of personality and psychological well-being on two broad affect components of subjective well-being

Subjective well-being (SWB) is defined in terms of positive and negative affect whilst psychological well-being (PWB) reflects self-referent attitudes of mastery and self-acceptance. Whilst both SWB and PWB are associated with personality, concurrent analysis is limited. This study (n = 679) reports on a teacher sample in which personality, SWB and PWB were measured. Results indicated moderate correlations between variables. Hierarchical regression controlled for personality and identified PWB as a significant predictor of SWB. Separate predictors of negative and positive affect support the need to assess both SWB affective components. As the most significant predictor of positive affect the inclusion of PWB is needed in future well-being research.     

N-of-1 study of weight loss maintenance assessing predictors of physical activity,adherence to weight loss plan and weight change

Objective: Behaviour change interventions are effective in supporting individuals to achieve clinically significant weight loss, but weight loss maintenance (WLM) is less often attained. This study examined predictive variables associated with WLM.

Design: N-of-1 study with daily ecological momentary assessment combined with objective measurement of weight and physical activity, collected with wireless devices (Fitbit?) for six months. Eight previously obese adults who had lost over 5% of their body weight in the past year took part. Data were analysed using time series methods.

Main outcomes measures: Predictor variables were based on five theoretical themes: maintenance motives, self-regulation, personal resources, habits, and environmental influences. Dependent variables were: objectively estimated step count and weight, and self-reported WLM plan adherence.

Results: For all participants, daily fluctuations in self-reported adherence to their WLM plan were significantly associated with most of the explanatory variables, including maintenance motivation and satisfaction with outcomes, self-regulation, habit, and stable environment. Personal resources were not a consistent predictor of plan adherence.

Conclusion: This is the first study to assess theoretical predictions of WLM within individuals. WLM is a dynamic process including the interplay of motivation, self-regulation, habit, resources, and perceptions of environmental context. Individuals maintaining their weight have unique psychological profiles which could be accounted for in interventions.     

Job stressors,Type A behavior,coping responses,and psychological burnout among teachers

This study examined a research model developed to understand psychological burnout in work settings. Data were collected from 473 teachers and school administrators using questionnaires completed anonymously. Four groups of predictor variables identified in previous research were considered: individual demographic and situational variables, Type A behavior, job Stressors and coping responses. Type A behavior, job Stressors and coping responses were significantly and independently related to levels of psychological burnout.     

Does habit strength moderate the intention–behaviour relationship in the Theory of Planned Behaviour? The case of fruit consumption

The present study examined if habit strength moderated the influence of intention on fruit consumption in a Dutch adult sample (N?=?521, 46.3% males, mean age?=?34.50, SD?=?10.87), using the theoretical relations of the Theory of Planned Behaviour (TPB). TPB variables and habit strength were assessed at baseline. Fruit consumption was assessed with a validated questionnaire five weeks later. Three groups were created: low habit strength (n?=?180), medium habit strength (n?=?185) and high habit strength (n?=?156). Confirmatory factor analyses and multi-group path analyses were performed using AMOS 4.0. A good fit was obtained for the overall measurement model and the structural models. Multi-group path analyses showed that intention was a significant predictor of fruit consumption in the low habit (β?=?0.36, p?<?0.001) and medium habit group (β?=?0.30, p?<?0.001), but a non-significant predictor in the high habit group (β?=?0.05, p?=?0.596). Implications for information-based and motivation-based interventions are discussed.