An Instrumental Variable Estimator for Mixed Indicators: Analytic Derivatives and Alternative Parameterizations

Methodological development of the model-implied instrumental variable (MIIV) estimation framework has proved fruitful over the last three decades. Major milestones include Bollen's (Psychometrika 61(1):109-121, 1996) original development of the MIIV estimator and its robustness properties for continuous endogenous variable SEMs, the extension of the MIIV estimator to ordered categorical endogenous variables (Bollen and Maydeu-Olivares in Psychometrika 72(3):309, 2007), and the introduction of a generalized method of moments estimator (Bollen et al., in Psychometrika 79(1):20-50, 2014). This paper furthers these developments by making several unique contributions not present in the prior literature: (1) we use matrix calculus to derive the analytic derivatives of the PIV estimator, (2) we extend the PIV estimator to apply to any mixture of binary, ordinal, and continuous variables, (3) we generalize the PIV model to include intercepts and means, (4) we devise a method to input known threshold values for ordinal observed variables, and (5) we enable a general parameterization that permits the estimation of means, variances, and covariances of the underlying variables to use as input into a SEM analysis with PIV. An empirical example illustrates a mixture of continuous variables and ordinal variables with fixed thresholds. We also include a simulation study to compare the performance of this novel estimator to WLSMV.

AnthropMMD: An R package with a graphical user interface for the mean measure of divergence

The mean measure of divergence is a dissimilarity measure between groups of individuals described by dichotomous variables. It is well suited to datasets with many missing values, and it is generally used to compute distance matrices and represent phenograms. Although often used in biological anthropology and archaeozoology, this method suffers from a lack of implementation in common statistical software. A package for the R statistical software, AnthropMMD, is presented here. Offering a dynamic graphical user interface, it is the first one dedicated to Smith's mean measure of divergence. The package also provides facilities for graphical representations and the crucial step of trait selection, so that the entire analysis can be performed through the graphical user interface. Its use is demonstrated using an artificial dataset, and the impact of trait selection is discussed. Finally, AnthropMMD is compared to three other free tools available for calculating the mean measure of divergence, and is proven to be consistent with them.

Revisiting the Phenice technique sex classification results reported by MacLaughlin and Bruce (1990)

Phenice (Am J Phys Anthropol 30 (1969):297-301) reported a success rate of 96% for his method of sex determination based on three morphological features of the pelvis. Numerous studies have tested and evaluated the method with affirmative results. The results of the study by MacLaughlin and Bruce (J Forensic Sci 35 (1990):1384-1392) were inconsistent with other studies, reporting far lower rates of accuracy and a greater degree of interobserver error. The authors believe that this may be the result of the inclusion of an "ambiguous" classification category. Revised modelling using forced classification of sex provides much higher classification rates with the implication that the poor results reported by MacLaughlin and Bruce were due to methodological error for the most part.

CFA with binary variables in small samples: a comparison of two methods

Asymptotically optimal correlation structure methods with binary data can break down in small samples. A new correlation structure methodology based on a recently developed odds-ratio (OR) approximation to the tetrachoric correlation coefficient is proposed as an alternative to the LPB approach proposed by Lee et al. (1995). Unweighted least squares (ULS) estimation with robust standard errors and generalized least squares (GLS) estimation methods were compared. Confidence intervals and tests for individual model parameters exhibited the best performance using the OR approach with ULS estimation. The goodness-of-fit chi-square test exhibited the best Type I error control using the LPB approach with ULS estimation.