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      The Utility and Application of Mixed-Effects Models in Second Language Research : Mixed-Effects Models

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      Language Learning
      Wiley-Blackwell

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          Conclusions beyond support: overconfident estimates in mixed models

          Mixed-effect models are frequently used to control for the nonindependence of data points, for example, when repeated measures from the same individuals are available. The aim of these models is often to estimate fixed effects and to test their significance. This is usually done by including random intercepts, that is, intercepts that are allowed to vary between individuals. The widespread belief is that this controls for all types of pseudoreplication within individuals. Here we show that this is not the case, if the aim is to estimate effects that vary within individuals and individuals differ in their response to these effects. In these cases, random intercept models give overconfident estimates leading to conclusions that are not supported by the data. By allowing individuals to differ in the slopes of their responses, it is possible to account for the nonindependence of data points that pseudoreplicate slope information. Such random slope models give appropriate standard errors and are easily implemented in standard statistical software. Because random slope models are not always used where they are essential, we suspect that many published findings have too narrow confidence intervals and a substantially inflated type I error rate. Besides reducing type I errors, random slope models have the potential to reduce residual variance by accounting for between-individual variation in slopes, which makes it easier to detect treatment effects that are applied between individuals, hence reducing type II errors as well.
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            Multilevel models for the experimental psychologist: foundations and illustrative examples.

            Although common in the educational and developmental areas, multilevel models are not often utilized in the analysis of data from experimental designs. This article illustrates how multilevel models can be useful with two examples from experimental designs with repeated measurements not involving time. One example demonstrates how to properly examine independent variables for experimental stimuli or individuals that are categorical, continuous, or semicontinuous in the presence of missing data. The second example demonstrates how response times and error rates can be modeled simultaneously within a multivariate model in order to examine speed-accuracy trade-offs at the experimental-condition and individual levels, as well as to examine differences in the magnitude of effects across outcomes. SPSS and SAS syntax for the examples are available electronically.
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              An overview of mixed-effects statistical models for second language researchers

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                Author and article information

                Journal
                Language Learning
                Language Learning
                Wiley-Blackwell
                00238333
                June 2015
                June 2015
                : 65
                : S1
                : 185-207
                Article
                10.1111/lang.12117
                ee96efa2-41f2-4aaf-86ce-f4335c9dc5c3
                © 2015

                http://doi.wiley.com/10.1002/tdm_license_1.1

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