Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs

Using a Monte Carlo simulation and the Kenward–Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. However, with heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null, the best fit was shown by the between-subjects heterogeneous unstructured population matrix, which was the case for all of the distributions analyzed. By contrast, with positive or negative pairings, the within-subjects and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased—as occurs, for example, in the log-normal distribution—the robustness of KR was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis, the analysis showed that the degree of robustness increased in line with the amount of kurtosis.     

Coping strategies and depression in Puerto Rican adolescents: an exploratory study

The use of inadequate coping strategies in stressful situations results in the development of depression in adolescents. This study identified coping strategies used by Puerto Rican adolescents and evaluated the relationship between coping and depression. Fifty-one adolescents participated in the study. Results indicated that the most frequently used coping strategy was developing positive perceptions about life situations. Significant differences were observed according to the severity of depressive symptoms. Investing in family relationships and developing positive perceptions about life situations seemed to reduce depression. Furthermore, the strategies of investing in family relationships and relieving tension through diversion were the variables with more predictive value for depression. The importance of exploring coping responses within the cultural context of the adolescent is discussed.     

Generalized Communicative Suspicion (GCS) Among Police Officers: Accounting for the Investigator Bias Effect1

Research shows that police officers are no more accurate than non‐officers in discerning between truthful and deceptive statements, but more biased than non‐officers to judge statements as deceptive. This was labeled by Meissner and Kassin (2002) as the investigator bias effect. A likely explanation could be that, since officers are normally involved in situations where questioning the truthfulness of the interviewee is essential, they could develop a generalized communicative suspicion (GCS). Levine and McCornack's (1991) GCS scale was adapted to the Spanish context and used to compare the GCS ratings of 152 undergraduates, 88 experienced officers, and 89 police recruits. Experienced officers’ GCS scores were significantly higher than those of the other groups, which did not differ from each other. This suggests that socialization within the police force increases the officers’ suspicion, leading them to make deceptiveness judgments.     

Median decision techniques as an alternative to the classical statistical inference test

In the research area, the criterion to test a hypothesis is frequently the distance of each subject from the mean of the distribution. This concept of distance is constantly used and re-used as a source of evidence in the search for significant contrasts with respect to models of theoretical probability. This paper proposes a number of ideas regarding the use of new distance indicators related to statistics that rely less heavily on parametric assumptions, in particular, the use of median confidence intervals. We have simulated via EXCEL different data samples for a design of two independent groups under 15 different conditions in two different situations: mean equality and mean differences. The results showed the high sensitivity of the comparison of the confidence intervals, especially if a strict decision criterion is used. However, we did not obtain good results for sensitivity. In fact, in some cases, the comparison of the confidence intervals of the mean worked better than those of median.     

Exercise motivation in university community members: a behavioural intervention

The purpose of this study was to examine how exercise level, exercise motives, and barriers changed from the baseline phase to the follow-up phase after a behavioural and cognitive intervention aimed at increasing exercise. Seventy-five members of our university community (43 subjects in the control group and 32 in the experimental group), all of whom received cognitive feedback, agreed to complete the baseline phase. Only the experimental group received behavioural feedback and a free-access gym ticket with personal training in order to facilitate their adherence to exercise. The results suggest that a combination of behavioural and psychological techniques is an efficient strategy for increasing exercise level. In addition, the results showed that extrinsic motivation predominates the early stages of change-of-exercise behaviour, and that intrinsic motivation is important for progression towards maintenance. Subjects who decreased their exercise level increased their extrinsic exercise motivation and subjects who increased their exercise level decreased the barriers related to intrinsic motivation. These findings indicate that, in order to facilitate exercise adherence, feedback about motives for undertaking exercise is needed, combined with advice about how to improve physical condition. This combination could help eliminate certain barriers that hinder engaging in an active and healthy life-style.     

Evaluating effects in short time series: alternative models of analysis

In the applied context, short time-series designs are suitable to evaluate a treatment effect. These designs present serious problems given autocorrelation among data and the small number of observations involved. This paper describes analytic procedures that have been applied to data from short time series, and an alternative which is a new version of the generalized least squares method to simplify estimation of the error covariance matrix. Using the results of a simulation study and assuming a stationary first-order autoregressive model, it is proposed that the original observations and the design matrix be transformed by means of the square root or Cholesky factor of the inverse of the covariance matrix. This provides a solution to the problem of estimating the parameters of the error covariance matrix. Finally, the results of the simulation study obtained using the proposed generalized least squares method are compared with those obtained by the ordinary least squares approach. The probability of Type I error associated with the proposed method is close to the nominal value for all values of rho1 and n investigated, especially for positive values of rho1. The proposed generalized least squares method corrects the effect of autocorrelation on the test's power.     

Autocorrelation problems in short time series

The work of Huitema (1985) on autocorrelation in behavioral data suggests that the use of conventional statistical methods is justified. The present study restates the problem of autocorrelation by analyzing 100 baselines of small samples designs published in the Journal of Applied Behavior Analysis during 1992. The results show a negative bias in the autocorrelations, especially with very small samples. The autocorrelation values are normally distributed, and the method of Davies, Trigg, and Newbold (1977) is the most accurate in calculating the standard deviation.     

Sex differences in functional brain activation during a lexical visual field task

Functional MRI was used to investigate sex differences in brain activation during a paradigm similar to a lexical-decision task. Six males and 6 females performed two runs of the lexical visual field task (i.e., deciding which visual field a word compared with a pseudoword was presented to). A sex difference was noted behaviorally: The reaction time data showed males had a marginal right visual field advantage and women a left visual field advantage. Imaging results showed that men had a strongly left-lateralized pattern of activation, e.g., inferior frontal and fusiform gyrus, while women showed a more symmetrical pattern in language related areas with greater right-frontal and right-middle-temporal activation. The data show evidence of task-specific sex differences in the cerebral organization of language processing.     

Should we rely on the Kenward–Roger approximation when using linear mixed models if the groups have different distributions?

The study explores the robustness to violations of normality and sphericity of linear mixed models when they are used with the Kenward–Roger procedure (KR) in split‐plot designs in which the groups have different distributions and sample sizes are small. The focus is on examining the effect of skewness and kurtosis. To this end, a Monte Carlo simulation study was carried out, involving a split‐plot design with three levels of the between‐subjects grouping factor and four levels of the within‐subjects factor. The results show that: (1) the violation of the sphericity assumption did not affect KR robustness when the assumption of normality was not fulfilled; (2) the robustness of the KR procedure decreased as skewness in the distributions increased, there being no strong effect of kurtosis; and (3) the type of pairing between kurtosis and group size was shown to be a relevant variable to consider when using this procedure, especially when pairing is positive (i.e., when the largest group is associated with the largest value of the kurtosis coefficient and the smallest group with its smallest value). The KR procedure can be a good option for analysing repeated‐measures data when the groups have different distributions, provided the total sample sizes are 45 or larger and the data are not highly or extremely skewed.     

Academic Plagiarism: Explanatory Factors from Students’ Perspective

The study of academic plagiarism among university students is at an embryonic stage in Spain and in the other Spanish-speaking countries. This article reports the results of a research, carried out in a medium-sized Spanish university, based on a double method approach—quantitative and qualitative—concerning the factors associated with academic plagiarism from the students’ perspective. The main explanatory factors of the phenomenon, according to the results obtained, are: a) aspects and behaviour of students (bad time management, personal shortcomings when preparing assignments, the elevated number of assignments to be handed in, etc.); b) the opportunities conferred by information and communication technologies to locate, copy and paste information; and, finally, c) aspects related to professors-lecturers and/or the characteristics of the subject-course (lecturers who show no interest in their work, eminently theoretical subjects and assignments, etc.).