Limitations of previous Studies

Overall, the picture these two studies provide is inconclusive, as disjunct aspects of the RMI were probed. The Kiesel et al. (2007) study for example has no coactivation implementation and thus cannot investigate power or a potential estimation bias of the RMI test in the coactivated case. Furthermore, as it employs a descriptive (instead of a

mechanistic) model of response times, it cannot illuminate the effects of base time on type I errors, power and the estimation bias. To generate their reaction time data, Kiesel et al. used the ex-Wald distribution, which is the convolution of an inverse Gaussian distribution with an exponential distribution. It is commonly used in experimental psychology to model reaction time data, and its parameters were believed to reflect the reaction time decomposition (with the inverse Gaussian or Wald-part being a model for the decision time and the exponential part signifying the base time component). The use of the ex-Wald and other distribution functions beyond the level of data description is problematic, as Matzke and Wagenmakers (2009) could show that the parameters of these models do not uniquely correspond to parameter changes of the theoretical and explicit model of reaction times. Townsend and Honey (2007) also used simplified, atheoretic response time models with empirically implausible distributions. Townsend and Honey use normally distributed data for their processing times data, which in contrast to right-skewed empirical reaction times is

symmetrical around its modus. This data is convolved with a normally distributed base time. Apart from these numerical issues, the studies are improvable in several other

respects. Neither Townsend nor Kiesel implemented differentially correlated race models, but instead only use the extremal case of race models (i.e. maximally negatively correlated racers). Neither study investigated both low and high sample sizes, different significance levels of the inner t-test, subject sizes or correlation and coactivation strengths (respectively). This is necessary, as the knowledge of these parameters can effectively help setting up the

RMI test in an optimal sense (e.g. minimizing type I errors or maximizing power rates or a combination of the two). Most importantly, the Townsend and Honey study did not look into type I error accumulation or the estimation bias, while the Kiesel et al. study neglects power and base time manipulations altogether.

4.1.5 Research Questions

Both these studies make valid and important points, every researcher applying the RMI tests should incorporate in their design and analysis. Nevertheless, the validity of these results relies on their replication and extension within an integrated and fully crossed study. This simulation study aims at integrating and extending the work and scope of the preceding studies in a coherent and adaptive framework. Specifically, this study addresses the

following open research questions: (a) What is the power of the RMI test, (b) is there an estimation bias in the RMI test when the data is actually coactivated (and if so, in what direction)? (c) what is the effect of base time variance on estimation bias, type I error accumulation, and power, and (d) are the results by Kiesel et al. (2007) and Townsend & Honey (2007) quantitatively or at least qualitatively replicable, when using mechanistic models instead of descriptive models of decision making? Table 4.1 gives an overview of the properties of previous simulation studies in comparison to the present study.

The RMI test has been introduced as a tool to elucidate the architecture question of multisensory integration. The results and inferences of RMI studies then are only as credible and solid as is the understanding of the tool that brings them about. In case of the RMI test, there are several known shortcomings, as were outlined so far. This simulation study aims at overcoming these issues and providing a means to assess the properties and performance of the RMI test in a principled way. It features the latest and most established models of decision making and will effectively improve both the knowledge on the RMI test and its application in an experimental context.

Table 4.1

Comparison of Scopes and Properties of Simulation Studies on the RMI Test.

Properties Study

Kiesel et al. (2007) Townsend &

Honey (2007) The present Study

Scope

Estimation Bias for Race; Type I Error Accumulation

Effects of Base Time Variance on Type I Errors and Power

Estimation Bias for Race and Coactivation; Type I Errors for correlated Racers; Power of latent and manifest Coactivation Alpha error/

accumulation X / X X / -- X / X

Race model ex-Wald distributed

normally, exponentially distributed

Ratcliff Diffusion Models

Interchannel

Correlation -1 (not specified) 0, -0.5, and -1

a Power -- X X Coactivation Model -- normally distributed (mean shifted)

decisional model (drift rate summation) Estimation Bias Race/ Coactivation X / -- -- / -- X / X Range of Sample Size 10, 20, and 40 100, 250, and 500 10, 20, 40, 100, 200, and 400

Subject Size 20, 40 1 8, 20, and 40

Notes. X denotes a present and -- denotes missing aspects in the respective study. a nominal values of interchannel correlation only, the effective

correlation lower due to the skewness of reaction time distributions. The present study integrated the scopes and parameters of interest into a coherent simulation framework.

4.2 Method