A Multilevel Multivariate Analysis of Academic Performances in College Based on NCAA Student-Athletes

This is an application of contemporary multilevel regression modeling to the prediction of academic performances of 1st-year college students. At a first level of analysis, the data come from N > 16,000 students who were college freshman in 1994–1995 and who were also participants in high-level college athletics. At a second level of analysis, the student data were related to the different characteristics of the C = 267 colleges in Division I of the NCAA. The analyses presented here initially focus on the prediction of freshman GPA from a variety of high school academic variables. The models used are standard multilevel regression models, but we examine nonlinear prediction within these multilevel models, and additional outcome variables are considered. The multilevel results show that (a) high school grades are the best available predictors of freshman college grades, (b) the ACT and SAT test scores are the next best predictors available, (c) the number of high school core units taken does not add to this prediction but does predict credits attained, (d) college graduation rate has a second-level effect of a small negative outcome on the average grades, and (e) nonlinear models indicate stronger effects for students at higher levels of the academic variables. These results show that standard multilevel models are practically useful for standard validation studies. Some difficulties were found with more advanced uses and interpretations of these techniques, and these problems lead to suggestions for further research.     

Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.     

The prediction of intelligence in preschool children using alternative models to regression

Statistical prediction of an outcome variable using multiple independent variables is a common practice in the social and behavioral sciences. For example, neuropsychologists are sometimes called upon to provide predictions of preinjury cognitive functioning for individuals who have suffered a traumatic brain injury. Typically, these predictions are made using standard multiple linear regression models with several demographic variables (e.g., gender, ethnicity, education level) as predictors. Prior research has shown conflicting evidence regarding the ability of such models to provide accurate predictions of outcome variables such as full-scale intelligence (FSIQ) test scores. The present study had two goals: (1) to demonstrate the utility of a set of alternative prediction methods that have been applied extensively in the natural sciences and business but have not been frequently explored in the social sciences and (2) to develop models that can be used to predict premorbid cognitive functioning in preschool children. Predictions of Stanford–Binet 5 FSIQ scores for preschool-aged children is used to compare the performance of a multiple regression model with several of these alternative methods. Results demonstrate that classification and regression treesprovided more accurate predictions of FSIQ scores than does the more traditional regression approach. Implications of these results are discussed.     

The obligation to succeed when it matters the most–The influence of skill and pressure on the success in football penalty kicks

In order to gain a more comprehensive understanding of the influence of skill and pressure on the success in football penalty kicks, we analyzed 1711 penalties taken over a 15-year period in major international tournaments. We conducted a multiple correspondence analysis in order to reduce six variables that are associated with skill and pressure to two dimensions that reflect our target concepts. Then, we used these two factors as independent variables in a logistic regression and fit different models using three binary dependent variables. The results show that high situational pressure significantly increases the probability of missing the goal entirely by about 6%, independent of the player’s skill level. The probability that the goalkeeper saves a penalty significantly decreases by roughly 4% when a highly skilled player takes the shot. In general, high situational pressure decreases the probability of scoring a penalty kick. Furthermore, the probability to score a penalty increases if a highly skilled player takes the kick which indicates that a high skill level can act as a kind of buffer against debilitating effects caused by performance pressure.     

Adjusting researchers’ approach to adjustment: On the use of covariates when testing interactions

A common design in social psychology involves the use of two independent variables, an experimental manipulation and a measured individual difference, and the interest is in the interaction between them. In such designs, there are often obvious covariate(s), correlated with the measured independent variable, which the researcher wishes to control. Typically this is done by including the covariate in the analytic model. We show that in most cases this is an inadequate model. In general, the interaction between the two independent variables will be estimated without bias only when the interaction between the covariate and the manipulated independent variable is included in the analysis. We present simulations showing the factors affecting the magnitude of the bias and provide a survey of recent social psychological literature illustrating the frequency of the problem. Finally, we discuss cases where both independent variables are manipulated and the covariate is a potential mediator.     

How the 2SLS/IV estimator can handle equality constraints in structural equation models: A system‐of‐equations approach

Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non‐iterative, equation‐by‐equation estimator that uses instrumental variables. Although this two‐stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models.     

An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log–likelihood of nonlinear state–space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple–subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.     

Children's use of addition to solve two‐digit subtraction problems

Subtraction problems of the type M ? S = ? can be solved with various mental calculation strategies. We investigated fourth‐ to sixth‐graders' use of the subtraction by addition strategy, first by fitting regression models to the reaction times of 32 two‐digit subtractions. These models represented three different strategy use patterns: the use of direct subtraction, subtraction by addition, and switching between the two strategies based on the magnitude of the subtrahend. Additionally, we compared performance on problems presented in two presentation formats, i.e., a subtraction format (81 ? 37 = .) and an addition format (37 + . = 81). Both methods converged to the conclusion that children of all three grades switched between direct subtraction and subtraction by addition based on the combination of two features of the subtrahend: If the subtrahend was smaller than the difference, direct subtraction was the dominant strategy; if the subtrahend was larger than the difference, subtraction by addition was mainly used. However, this performance pattern was only observed when the numerical distance between subtrahend and difference was large. These findings indicate that theoretical models of children's strategy choices in subtraction should include the nature of the subtrahend as an important factor in strategy selection.     

Predicting Success in Vocational Training By Using the GATB

This study examined the relationship between the General Aptitude Test Battery (GATB)and class performance of eleventh- and twelfth-grade high school students enrolled in the Current River Area Vocational School, Doniphan, Missouri. Teachers' grades were used as the dependent variable, and the nine independent variables were scores taken from the aptitude factors of the GATB. The stepwise multiple regression technique was used to determine the optimal set of predictors to be used in establishing a regression equation. The results of the project should help in counseling prospective trainees toward trade or shop areas and tentative vocational planning. If not used out of perspective, the G variable in the GATB was the best single predictor of success; the best combination of variables was the G, N, P, F, and M aptitude factors.     

The influence of personality and theoretical models on applicants to a counselling psychology course: A preliminary study

We examined whether personality variables in prospective condidates for a postgraduate program in counselling psychology were associated with an interest in models of counselling or therapy. The models were classified as directive models or non-deiective models of counselling. Using the Millon Index of Personality Styles we found that subjects who expressed an interest in the directive models of counselling (e.g. cognitive behavioural therapy) scored higher on scales measuring interpersonal boldness, systematizing and conforming in comparison to subjects who expressed an interest in non-dieective counselling (e.g. psychodynamic) who scored greater on intuitiveness (a perference for intangible, unstructured and symbolic). Implication for training and future research in this area are discussed.     

Predicting Academic Achievement with the High School Placement Test

The study reported here investigated the use of the High School Placement Test as a predictor of 9th grade academic achievement as measured by school grades. The sample was composed of 3,194 boys who were enrolled in an academic curriculum at 1 of the 10 randomly selected Diocesan high schools in Philadelphia. A multiple regression analysis and a canonical correlation analysis were performed using the subtest scores of the High School Placement Test as independent variables, and final 9th grade average, grades in English, social studies, Latin, general science, and algebra as the dependent variables. It was found that the Composite score of the High School Placement Test individually would have been as useful a predictor of final grades as either of the empirically determined predictor composites computed in performing the multiple regression analysis and the canonical correlation analysis.     

词频和年级对FOK判断的影响

本实验以识记材料的词频高低和被试年级为自变量对被试元记忆监测的FOK(feeling of knowing)判断进行研究。实验采用Hart提出的RJR(回忆—FOK判断—标准测验 )的经典范式。结果表明 :被试的年级影响FOK判断等级和准确性 ,大学生的FOK判断等级和准确性均高于高一年级学生 ;识记材料词频影响FOK判断等级的高低 ,不影响FOK判断准确性 ,被试对高频词对的FOK判断等级高于对低频词对的FOK判断等级 ,但FOK判断准确性无明显差异。     

Using generalized additive (mixed) models to analyze single case designs

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.     

State-trace analysis can be an appropriate tool for assessing the number of cognitive systems: A reply to Ashby (2014)

Ashby (2014) has argued that state-trace analysis (STA) is not an appropriate tool for assessing the number of cognitive systems, because it fails in its primary goal of distinguishing single-parameter and multiple-parameter models. We show that this is based on a misunderstanding of the logic of STA, which depends solely on nearly universal assumptions about psychological measurement and clearly supersedes inferences based on functional dissociation and the analysis of interactions in analyses of variance. We demonstrate that STA can be used to draw inferences concerning the number of latent variables mediating the effects of a set of independent variables on a set of dependent variables. We suggest that STA is an appropriate tool to use when making arguments about the number of cognitive systems that must be posited to explain behavior. However, no statistical or inferential procedure is able to provide definitive answers to questions about the number of cognitive systems, simply because the concept of a “system” is not defined in an appropriate way.     

A hierarchical state space approach to affective dynamics

Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict-oriented interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on various components of this versatile model.     

Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors

We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, x (where x is an n×1 vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in n-dimensional space. For a full-rank predictor correlation matrix, R _xx, of order n, and for regression models with constant R ² (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an n-dimensional ellipsoid. The population performance of alternate regression weights—such as equal weights, correlation weights, or rounded weights—can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of R ². To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an n-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in ℝ ⁿ , and (3) populating the set of regression vectors that have constant cosine with a target vector in ℝ ⁿ . Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.     

Sleep variability and fatigue in adolescents: Associations with school‐related features

This study aims to evaluate the influences of sleep duration and sleep variability (SleepV), upon adolescents' school‐related situations. The Health Behaviour in School‐Aged Children (HBSC) survey is based on a self‐completed questionnaire. The participants were 3164 pupils (53.7% girls), attending the 8th and 10th grades, 14.9 years old, and were inquired about subjective sleep duration during the week and weekends, SleepV, fatigue, difficulties in sleep initiation, school achievement, feelings towards schools, pressure with school work and skipping classes. Multiple regression models used, as dependent variables: (a) school achievement, (b) disliking school, (c) pressure with school work and (d) skipping classes, using as independent variables, each of the remaining school‐related variables, fatigue, total sleep duration and difficulties in sleep initiation. The average sleep duration in the week and during weekdays was lower than recommended for these age groups, and almost half of students had high SleepV between weekdays and weekends. A logistic model revealed that the absence of SleepV was associated with lower perception of school work pressure, less frequent skipping classes, more infrequent fatigue and more infrequent difficulties in sleep initiation. Poor sleep quality, SleepV and insufficient sleep duration affected negatively school‐related variables.     

Extending Statistics of Extremes to Distributions Varying in Position and Scale and the Implications for Race Models

Race models are characterized by the largest or smallest of samples from n distributions. The asymptotic theory of extremes has demonstrated that for identically distributed, independent, and lower-bounded random variables, whose left tail approximates a power function, the distribution of the minimum tends toward a Weibull distribution as n increases. In this article, we remove the restriction of identically distributed random variables by letting the lower bound or the scale of the random variables be random variables themselves. We prove that the Weibull distribution is still the asymptotic distribution of the minimum and relate its parameters to the parameters of the input distributions. We discuss the potential use of such findings in models of psychological processes.     

Adoption vs. parenting decisions among pregnant adolescents

The choice of adoption is rare among pregnant adolescents. This exploratory study used regression analyses to ascertain which demographic, social, and intervention variables were related to this decision. The adolescents with mothers who favored adoption and/or had few parenting peer models were more likely to choose adoption. Age, knowledge of peers who had chosen adoption, grades in school, level of involvement in a comprehensive adolescent pregnancy program, and participation in individual therapy or Decision-Making Group were not significantly related to the decision. Decision-Making Group is a once-a-week therapy session that focuses on adoption vs. parenting decisions for pregnant adolescents. Eighty-seven percent of the adolescents who participated in these sessions found them helpful. The policy implications for adolescent pregnancy programs are explored.