Modeling number line data as mixture growth model within session

Young children's number line placements have been investigated often but it is not entirely clear how best to characterize particular strategies used and how strategy use in number line placement develops. In samples of younger children we expect to find a mix of four main strategies: (1) Random responding. (2) Adult like linear and accurate responding. (3) Responding biased by the zero boundary (key words: power law, logarithmic transformation). (4) Responding biased by lower and upper boundary of the line segment (keywords: proportional reasoning, logistic transformation). With development strategy 1 use will disappear, strategy 2 use will increase, strategy 3 and 4 use will decline. We reanalyzed an existing large longitudinal dataset (N=161, 6 waves). We applied mixture modeling for longitudinal data, as implemented in Mplus, for the repeated placements within a task session. We transformed the data and reformulated the strategies described above to particular slope trend expectations. It might be an unusual way to analyze the data but it works fine. The basic formulas are the same as used by Rouder and Geary (2014). However, we will present a more complete model. We expect that this analysis method can be easily used with any number line data set.