Determining whether a construct is more appropriately conceptualized and assessed in a categorical or a dimensional manner has received considerable research attention in recent years. There are a variety of statistical techniques to address this empirically, and Meehl's (1995) taxometric method has been among the most widely used methods applied to constructs in the areas of personality and psychopathology. In taxometric analysis, the comparison curve fit index (CCFI; Ruscio, Ruscio, & Meron, 2007) is an objective measure of whether parallel analysis of categorical or dimensional comparison data better reproduce empirical data results. The development and use of the CCFI helps to reduce the subjectivity involved in performing taxometric analyses and interpreting the results. In a series of simulation studies, we examine the use of the CCFI to flesh out some empirically supported guidelines. We find that a panel of curves should be averaged to calculate a single CCFI value (rather than calculating the CCFI for each curve and averaging these values), that an ambiguous range of CCFI values should be defined using a fixed-width interval (rather than a multiple of the estimated standard error), and that constructing a CCFI profile can help to differentiate categorical and dimensional data and provide a less biased and more precise estimate of the taxon base rate than conventional methods. Implications of these findings for taxometric research relevant to psychological assessment are discussed along with ways to perform analyses consistent with these recommendations. (PsycINFO Database Record

We prove prime geodesic theorems counting primitive closed geodesics on a compact hyperbolic 3-manifold with length and holonomy in prescribed intervals, which are allowed to shrink. Our results imply effective equidistribution of holonomy and have both the rate of shrinking and the strength of the error term fully symmetric in length and holonomy.

Ambient prime geodesic theorems provide an asymptotic count of closed geodesics by their length and holonomy and imply effective equidistribution of holonomy. We show that for a smoothed count of closed geodesics on compact hyperbolic 3-manifolds, there is a persistent bias in the secondary term which is controlled by the number of zero spectral parameters. In addition, we show that a normalized, smoothed bias count is distributed according to a probability distribution, which we explicate when all distinct, non-zero spectral parameters are linearly independent. Finally, we construct an example of dihedral forms which does not satisfy this linear independence condition.