A two‐part mixed effects model for cigarette purchase task data

The Cigarette Purchase Task is a behavioral economic assessment tool designed to measure the relative reinforcing efficacy of cigarette smoking across different prices. An exponential demand equation has become a standard model for analyzing purchase task data, but its utility is compromised by its inability to accommodate values of zero consumption. We propose a two‐part mixed effects model that keeps the same exponential demand equation for modeling nonzero consumption values, while providing a logistic regression for the binary outcome of zero versus nonzero consumption. Therefore, the proposed model can accommodate zero consumption values and retain the features of the exponential demand equation at the same time. As a byproduct, the logistic regression component of the proposed model provides a new demand index, the “derived breakpoint”, for the price above which a subject is more likely to be abstinent than to be smoking. We apply the proposed model to data collected at baseline from college students (N = 1,217) enrolled in a randomized clinical trial utilizing financial incentives to motivate tobacco cessation. Monte Carlo simulations showed that the proposed model provides better fits than an existing model. We note that the proposed methodology is applicable to other purchase task data, for example, drugs of abuse.     

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.     

A Comparative Investigation of Confidence Intervals for IndependentVariables in Linear Regression

In linear regression, the most appropriate standardized effect size for individual independent variables having an arbitrary metric remains open to debate, despite researchers typically reporting a standardized regression coefficient. Alternative standardized measures include the semipartial correlation, the improvement in the squared multiple correlation, and the squared partial correlation. No arguments based on either theoretical or statistical grounds for preferring one of these standardized measures have been mounted in the literature. Using a Monte Carlo simulation, the performance of interval estimators for these effect-size measures was compared in a 5-way factorial design. Formal statistical design methods assessed both the accuracy and robustness of the four interval estimators. The coverage probability of a large-sample confidence interval for the semipartial correlation coefficient derived from Aloe and Becker was highly accurate and robust in 98% of instances. It was better in small samples than the Yuan-Chan large-sample confidence interval for a standardized regression coefficient. It was also consistently better than both a bootstrap confidence interval for the improvement in the squared multiple correlation and a noncentral interval for the squared partial correlation.     

Imagining an ‘ideal school’: an approach for reflecting on principals’ educational creed

In this paper, we describe an approach to the study and development of school principals’ school creed. The approach and its underlying method are grounded in the phenomenological tradition, predominantly in the philosophy of Merleau-Ponty. School principals are asked to imagine an ideal school and present it both visually and verbally. We illustrate the potential of this process using one ideal school proposal developed by a high school principal in Israel. The paper concludes with a discussion of the implications of the approach for research, theory and practice.     

Health‐adjusted neuropsychological test norms based on 463 older Swedish car drivers

There is a need for improved normative information in particular for older persons. The present study provides neuropsychological test norms on seven cognitive tests used in a sample representing the general older driving population, when uncontrolled and controlled for physical health. A group of 463 healthy Swedish car drivers, aged 65 to 84 years, participated in a medical and neuropsychological examination. The latter included tests of visual scanning, mental shifting, visual spatial function, memory, reaction time, selective attention, and simultaneous capacity. Hierarchical regression analyses demonstrated that, when uncontrolled for health, old age was associated with significant impairment on all seven tests. Education was associated with a significant advantage for all tests except most reaction time subtests. Women outperformed men on selective attention. Controlling for health did not consistently change the associations with education, but generally weakened those with age, indicating rises in normative scores of up to 0.36 SD (residual). In terms of variance explained, impaired health predicted on average 2.5%, age 2.9%, education 2.1% and gender 0.1%. It was concluded (1) that individual regression‐based predictions of expected values have the advantage of allowing control for the impact of health on normative scores in addition to the adjustment for various demographic and performance‐related variables and (2) that health‐adjusted norms have the potential to classify functional status more accurately, to the extent that these norms diverge from norms uncontrolled for physical health.     

Some relationships between factors and components

The asymptotic correlations between the estimates of factor and component loadings are obtained for the exploratory factor analysis model with the assumption of a multivariate normal distribution for manifest variables. The asymptotic correlations are derived for the cases of unstandardized and standardized manifest variables with orthogonal and oblique rotations. Based on the above results, the asymptotic standard errors for estimated correlations between factors and components are derived. Further, the asymptotic standard error of the mean squared canonical correlation for factors and components, which is an overall index for the closeness of factors and components, is derived. The results of a Monte Carlo simulation are presented to show the usefulness of the asymptotic results in the data with a finite sample size.The author is indebted to anonymous referees for their comments, corrections and suggestions which have led to the improvement of this article.     

影响儿童至老年人“位置法”记忆训练效果的因素探析

１１８名儿童、少年、青年、中年和老年被试参加＂位置法＂记忆训练,在训练前后对被试进行了一些认知功能的测查,以探讨被试的年龄及认知能力诸因素对记忆训练效果的影响及其预测性。结果表明：①训练前字词和图形记忆成绩、＂数字符号＂测验成绩与训练后记忆成绩相关极其显著,＂词汇＂测验成绩和想象力与训练后记忆成绩的相关也达到显著性水平;②年龄与训练后记忆效果的关系是非线性的;③除＂词汇＂成绩外,各项认知成绩均可预测训练后字词记忆成绩,训练后的图形记忆迁移效果可由＂数字符号＂测验成绩预测。     

Out-of-bag Prediction Error: A Cross Validation Index for Generalized Structured Component Analysis

Cross validation is a useful way of comparing predictive generalizability of theoretically plausible a priori models in structural equation modeling (SEM). A number of overall or local cross validation indices have been proposed for existing factor-based and component-based approaches to SEM, including covariance structure analysis and partial least squares path modeling. However, there is no such cross validation index available for generalized structured component analysis (GSCA) which is another component-based approach. We thus propose a cross validation index for GSCA, called Out-of-bag Prediction Error (OPE), which estimates the expected prediction error of a model over replications of so-called in-bag and out-of-bag samples constructed through the implementation of the bootstrap method. The calculation of this index is well-suited to the estimation procedure of GSCA, which uses the bootstrap method to obtain the standard errors or confidence intervals of parameter estimates. We empirically evaluate the performance of the proposed index through the analyses of both simulated and real data.     

A New Multilevel CART Algorithm for Multilevel Data with Binary Outcomes

The multilevel logistic regression model (M-logit) is the standard model for modeling multilevel data with binary outcomes. However, many assumptions and restrictions should be considered when applying this model for unbiased estimation. To overcome these limitations, we proposed a multilevel CART (M-CART) algorithm which combines the M-logit and single level CART (S-CART) within the framework of the expectation-maximization. Simulation results showed that the proposed M-CART provided substantial improvements on classification accuracy, sensitivity, and specific over the M-logit, S-CART, and single level logistic regression model when modeling multilevel data with binary outcomes. This benefit of using M-CART was consistently found across different conditions of sample size, intra-class correlation, and when relationships between predictors and outcomes were nonlinear and nonadditive.