A latent variable structural equation model was employed to test the goodness of fit of Garner's ``run--gap'' heuristic predictions to the data gathered from the two experiments. Figure 1 shows a path model of Garner's run--gap heuristics. The predictor variables are Run, the run principle, and Gap, the gap principle. The latent variable is S, the perceived structure of the rhythmic pattern. The measured outcome variables are RB, the response within the beat; A, the accuracy of the response; and V, the velocity of the response.
Figure 1: Path diagram showing a structural model of Garner's basic run--gap theory.
The Run variable is constructed as follows: if the current stimulus beat value is 1 and the previous stimulus beat value is 0, then Run = 1 + the number of stimulus beats following the current stimulus beat before another stimulus beat with a value of 0 is encountered. The Gap variable is constructed similarly: if the current stimulus beat value is 1 and the previous stimulus beat value is 0, then Gap = 1 + the number of stimulus beats preceding the current stimulus beat before a stimulus beat with a value of 1 is encountered.
The outcome variables were coded as follows. If a keypress occurred within of the onset of the current stimulus beat, then RB was coded as 1, otherwise as 0. If RB was 1, the MIDI velocity of the keypress (range 1--127) was coded as V. If RB was 1, A was coded as
where is the elapsed time to the keypress, is the elapsed time to the onset of the stimulus beat, and b is the duration of the beat. This means that the accuracy of the keypress was 1 if the keypress occurred simultaneously with the onset of the stimulus beat, and the accuracy was 0 if the keypress occurred halfway between two stimulus beats.
RM was coded as 0 if no keypress occurred within plus or minus one half measure of the current stimulus beat. Thus RM began the trial as a string of 0's and became a string of 1's when the subject began to respond to the stimulus.