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ABSTRACT: This study analyzes the robustness of the linear mixed model (LMM) with the Kenward-Roger (KR) procedure to violations of normality and sphericity when used in split-plot designs with small sample sizes. Specifically, it explores the independent effect of skewness and kurtosis on KR robustness for the values of skewness and kurtosis coefficients that are most frequently found in psychological and educational research data. To this end, a Monte Carlo simulation study was designed, considering a split-plot design with three levels of the between-subjects grouping factor and four levels of the within-subjects factor. Robustness is assessed in terms of the probability of type I error. The results showed that (1) the robustness of the KR procedure does not differ as a function of the violation or satisfaction of the sphericity assumption when small samples are used; (2) the LMM with KR can be a good option for analyzing total sample sizes of 45 or larger when their distributions are normal, slightly or moderately skewed, and with different degrees of kurtosis violation; (3) the effect of skewness on the robustness of the LMM with KR is greater than the corresponding effect of kurtosis for common values; and (4) when data are not normal and the total sample size is 30, the procedure is not robust. Alternative analyses should be performed when the total sample size is 30.
Behavior Research Methods 01/2013; · 2.12 Impact Factor
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ABSTRACT: This study aimed to evaluate the robustness of the linear mixed model, with the Kenward-Roger correction for degrees of freedom, when implemented in SAS PROC MIXED, using split-plot designs with small sample sizes. A Monte Carlo simulation design involving three groups and four repeated measures was used, assuming an unstructured covariance matrix to generate the data. The study variables were: sphericity, with epsilon values of 0.75 and 0.57; group sizes, equal or unequal; and shape of the distribution. As regards the latter, non-normal distributions were introduced, combining different values of kurtosis in each group. In the case of unbalanced designs, the effect of pairing (positive or negative) the degree of kurtosis with group size was also analysed. The results show that the Kenward-Roger procedure is liberal, particularly for the interaction effect, under certain conditions in which normality is violated. The relationship between the values of kurtosis in the groups and the pairing of kurtosis with group size are found to be relevant variables to take into account when applying this procedure.
Psicothema 08/2012; 24(3):449-54. · 1.02 Impact Factor
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ABSTRACT: 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.
Behavior Research Methods 03/2012; · 2.12 Impact Factor
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ABSTRACT: One of the procedures used most recently with longitudinal data is linear mixed models. In the context of health research the increasing number of studies that now use these models bears witness to the growing interest in this type of analysis. This paper describes the application of linear mixed models to a longitudinal study of a sample of Spanish adolescents attending a mental health service, the aim being to investigate their knowledge about the consumption of alcohol and other drugs. More specifically, the main objective was to compare the efficacy of a motivational interviewing programme with a standard approach to drug awareness. The models used to analyse the overall indicator of drug awareness were as follows: (a) unconditional linear growth curve model; (b) growth model with subject-associated variables; and (c) individual curve model with predictive variables. The results showed that awareness increased over time and that the variable 'schooling years' explained part of the between-subjects variation. The effect of motivational interviewing was also significant.
The Spanish journal of psychology 11/2011; 14(2):724-33. · 0.74 Impact Factor
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ABSTRACT: The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions about intervention effectiveness in single-case designs. Ordinary least square estimation is compared to two correction techniques dealing with general trend and a procedure that eliminates autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approach the nominal ones in the presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.
Psicothema 11/2010; 22(4):1026-32. · 1.02 Impact Factor
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ABSTRACT: Many areas of psychological, social, and health research are characterised by hierarchically structured data. Growth curves are usually represented by means of a two-level hierarchical structure in which observations are the first-level units nested within subjects, the second-level units. With data such as these, the best option for analysis is the general linear mixed model, which can be used even with longitudinal data series in which intervals are not constant or for which over the passage of time there is loss of data. In this paper an overview is given of the general linear mixed model approach to the analysis of longitudinal data in developmental research. The advantages of this model in comparison with the traditional approaches for analysing longitudinal data are shown, emphasising the usefulness of modelling the covariance structure properly to achieve a precise estimation of the parameters of the model.
Perceptual and Motor Skills 04/2010; 110(2):547-66. · 0.49 Impact Factor
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ABSTRACT: In this work, an innovative teaching model applied to methodological contents in psychology is presented. The proposed didactic model includes Information and Communication Technologies (ICT), such as CD-ROMs, web sites and Internet. These resources complement class attendance. In the classes the students are informed, guided and oriented so that they are able to obtain information and reorganize it in a coherent way. The aim of this article is to find out the students' learning preferences and estimate the incorporation of ICT, by means of the ETIM (Evaluation of Teaching Innovation Model) questionnaire. The results show that the students are aware of the need to consult other materials and that ICT helps students to understand the subject from various perspectives. In this way, the students become more autonomous in acquiring learning results.
Psicothema 09/2006; 18(3):646-51. · 1.02 Impact Factor
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ABSTRACT: 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.
Perceptual and Motor Skills 05/2004; 98(2):419-32. · 0.49 Impact Factor
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ABSTRACT: 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.
Psychological Reports 05/2003; 92(2):355-64. · 0.44 Impact Factor
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ABSTRACT: The conventional first-order autocorrelationcoefficient r1 generates an empiricalbias when it is applied to short time series.The properties of this estimator have beenexamined with a Monte Carlo simulation studyusing the MATLAB program (version5.2). This study also analyzes the functionof the empirical bias with the polynomicregression and derives a polynomic fittingmodel for different sample sizes. In thisway, a new estimator that has been correctedby the absolute value of the fitting model(r1') is proposed. Having analyzed thestatistical properties of the estimator r1',it is shown that the empirical bias generatedby r1' is less in relationship to r1 andr1+. The results of the study make itpossible to verify that the mean squared errorassociated to the estimator r1 isless than that of r1. Thus, the coefficient r1'is recommended to estimate the lag-oneautocorrelation coefficient in samples under 50observations.
Quality and Quantity 01/2001; 35(4):365-387. · 0.77 Impact Factor
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ABSTRACT: Young's C statistic (1941) makes it possible to compare the randomization of a set of sequentially organized data and constitutes an alternative of appropriate analysis in short time series designs. On the other hand, models based on the randomization of stimuli are also very important within the behavioral content applied. For this reason, a comparison is established between the C statistic and the Edgington model. The data analyzed in the comparative study have been obtained from graphs in studies published in behavioral journals. According to the results obtained, it is concluded that the Edgington model in experimental designs AB involves many measurements while the C statistic requires fewer observations to reach the conventional significance level.
Quality and Quantity 01/1998; 32(1):63-75. · 0.77 Impact Factor
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ABSTRACT: Técnicas fundamentadas en la regresión para la decisión estadística en diseños de caso único. El estudio evalúa el rendimiento de cuatro métodos de estimación de los coefi cientes de regresión utilizados para la toma de decisiones estadísticas sobre la efectividad de las intervenciones en diseños de caso único. La estimación por mínimos cuadrados ordinarios se compara con dos métodos que controlan la tendencia en los datos y un procedimiento que elimina la autocorrelación cuando ésta es signifi cativa. Los resultados indican que las tasas empíricas y nominales de falsas alarmas no coinciden en presencia de dependencia serial o tendencia al aplicar mínimos cuadrados ordinarios o generalizados. Los métodos que controlan la tendencia muestran tasas más bajas de error Tipo I, pero no son sufi cientemente sensibles a efectos existentes (cambio de nivel o de pendiente), por lo que el uso de la signifi cación estadística de los coefi cientes de regresión para detectar efectos no se recomienda cuando se dispone de series cortas de datos.
Psicothema, ISSN 0214-9915, Vol. 22, Nº. 4, 2010, pags. 1026-1032.
