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To transform or not to transform: using generalized linear mixed models to analyse reaction time data.

Lo S, Andrews S - Front Psychol (2015)

Bottom Line: Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions.For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT.We then consider the broader benefits of using GLMM to investigate individual differences.

View Article: PubMed Central - PubMed

Affiliation: School of Psychology, University of Sydney Sydney, NSW, Australia.

ABSTRACT
Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann (2013) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of normality. Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences.

No MeSH data available.


Related in: MedlinePlus

Prediction plots illustrating the estimated frequency effect and statistical results (t- or z-value and corresponding p-value) of the word frequency by stimulus quality interaction (shaded region on x-axis) based on models assuming an inverse relationship between the predictors and RT (inverse link function). The plots also present the back-transformed estimates (shaded region on y-axis) on the original RT metric. Each column of plots represents the results from a different experiment (from left to right: Yap and Balota, 2007; Yap et al., 2008: Experiment 1; and Yap et al., 2008: Experiment 2), and each row of plots represents a different assumption for the distribution of RTs (from top to bottom: Gaussian, Gamma, and Inverse Gaussian). Note that precise p-values are produced in GLMM for the Wald Z-statistic in R, while approximate p-values can only be inferred based on the magnitude of the t-value produced in LMM.
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Figure 4: Prediction plots illustrating the estimated frequency effect and statistical results (t- or z-value and corresponding p-value) of the word frequency by stimulus quality interaction (shaded region on x-axis) based on models assuming an inverse relationship between the predictors and RT (inverse link function). The plots also present the back-transformed estimates (shaded region on y-axis) on the original RT metric. Each column of plots represents the results from a different experiment (from left to right: Yap and Balota, 2007; Yap et al., 2008: Experiment 1; and Yap et al., 2008: Experiment 2), and each row of plots represents a different assumption for the distribution of RTs (from top to bottom: Gaussian, Gamma, and Inverse Gaussian). Note that precise p-values are produced in GLMM for the Wald Z-statistic in R, while approximate p-values can only be inferred based on the magnitude of the t-value produced in LMM.

Mentions: Figure 2 summarizes the predictions of the models assuming a linear relationship between the predictors and RT for the three experiments. The corresponding results for models assuming an inverse relationship between the predictors and RT are presented in Figure 4. Each column of Figures 2–5 corresponds to a different experiment, while the rows of the figures present estimates from the LMM models (top row), and GLMM models assuming Gamma (middle row), and Inverse Gaussian (bottom row) distributions, respectively, of the DV.


To transform or not to transform: using generalized linear mixed models to analyse reaction time data.

Lo S, Andrews S - Front Psychol (2015)

Prediction plots illustrating the estimated frequency effect and statistical results (t- or z-value and corresponding p-value) of the word frequency by stimulus quality interaction (shaded region on x-axis) based on models assuming an inverse relationship between the predictors and RT (inverse link function). The plots also present the back-transformed estimates (shaded region on y-axis) on the original RT metric. Each column of plots represents the results from a different experiment (from left to right: Yap and Balota, 2007; Yap et al., 2008: Experiment 1; and Yap et al., 2008: Experiment 2), and each row of plots represents a different assumption for the distribution of RTs (from top to bottom: Gaussian, Gamma, and Inverse Gaussian). Note that precise p-values are produced in GLMM for the Wald Z-statistic in R, while approximate p-values can only be inferred based on the magnitude of the t-value produced in LMM.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4528092&req=5

Figure 4: Prediction plots illustrating the estimated frequency effect and statistical results (t- or z-value and corresponding p-value) of the word frequency by stimulus quality interaction (shaded region on x-axis) based on models assuming an inverse relationship between the predictors and RT (inverse link function). The plots also present the back-transformed estimates (shaded region on y-axis) on the original RT metric. Each column of plots represents the results from a different experiment (from left to right: Yap and Balota, 2007; Yap et al., 2008: Experiment 1; and Yap et al., 2008: Experiment 2), and each row of plots represents a different assumption for the distribution of RTs (from top to bottom: Gaussian, Gamma, and Inverse Gaussian). Note that precise p-values are produced in GLMM for the Wald Z-statistic in R, while approximate p-values can only be inferred based on the magnitude of the t-value produced in LMM.
Mentions: Figure 2 summarizes the predictions of the models assuming a linear relationship between the predictors and RT for the three experiments. The corresponding results for models assuming an inverse relationship between the predictors and RT are presented in Figure 4. Each column of Figures 2–5 corresponds to a different experiment, while the rows of the figures present estimates from the LMM models (top row), and GLMM models assuming Gamma (middle row), and Inverse Gaussian (bottom row) distributions, respectively, of the DV.

Bottom Line: Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions.For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT.We then consider the broader benefits of using GLMM to investigate individual differences.

View Article: PubMed Central - PubMed

Affiliation: School of Psychology, University of Sydney Sydney, NSW, Australia.

ABSTRACT
Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann (2013) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of normality. Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. (2013) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences.

No MeSH data available.


Related in: MedlinePlus