On the explaining-away phenomenon in multivariate latent variable models

On Reverse Shrinkage Effects and Shrinkage Overshoot

Given a squared Euclidean norm penalty, we examine some less well-known properties of shrinkage estimates. In particular, we highlight that it is possible for some components of the shrinkage estimator to be placed further away from the prior mean than the original estimate. An analysis of this effect is provided within three different modeling settings-encompassing linear, logistic, and ordinal regression models. Additional simulations show that the outlined effect is not a mathematical artefact, but likely to occur in practice. As a byproduct, they also highlight the possibilities of sign reversals ("overshoots") for shrinkage estimates. We point out practical consequences and challenges, which might arise from the observed effects with special emphasis on psychometrics.

On Fair Person Classification Based on Efficient Factor Score Estimates in the Multidimensional Factor Analysis Model

Since Hooker, Finkelman and Schwartzman (Psychometrika 74(3): 419-442, 2009) it is known that person parameter estimates from multidimensional latent variable models can induce unfair classifications via paradoxical scoring effects. The open question as to whether there is a fair and at the same time multidimensional scoring scheme with adequate statistical properties is addressed in this paper. We develop a theorem on the existence of a fair, multidimensional classification scheme in the context of the classical linear factor analysis model and show how the computation of the scoring scheme can be embedded in the context of linear programming. The procedure is illustrated in the framework of scoring the Wechsler Adult Intelligence Scale (WAIS-IV).

A Generalized Speed-Accuracy Response Model for Dichotomous Items

We propose a generalization of the speed-accuracy response model (SARM) introduced by Maris and van der Maas (Psychometrika 77:615-633, 2012). In these models, the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled. Our generalization is similar to that of the one-parameter logistic (or Rasch) model to the two-parameter logistic (or Birnbaum) model in item response theory. An expectation-maximization (EM) algorithm for estimating model parameters and standard errors was developed. Furthermore, methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score. The presented methods were evaluated in a small simulation study, the results of which indicated good parameter recovery and reasonable type I error rates for the residuals. Finally, the methods were applied to two real data sets. It was found that the two-parameter SARM showed improved fit compared to the one-parameter SARM in both data sets.

Immune biomarkers are more accurate in prediction of survival in ulcerated than in non-ulcerated primary melanomas

INTRODUCTION

Ulcerated melanomas may have a unique biology and microenvironment. We test whether markers of immune infiltration correlate with clinical outcome in ulcerated compared to non-ulcerated primary melanoma tumors.

METHODS

Sixty-two stage II-III cutaneous melanomas, 32 ulcerated and 30 non-ulcerated, were analyzed for tumor-infiltrating lymphocytes (TILs). Immunohistochemistry (IHC) was performed for CD2, a marker previously shown to correlate with overall survival (OS) and recurrence-free survival (RFS) in this patient population. IHC using antibody, VE1, to BRAF V600E was also performed on a subset of 41 tumors to assess the relationship of BRAF mutation to immune markers.

RESULTS

We found, using Cox regression models, that the presence of TILs was associated with improved OS (p = 0.034) and RFS (p = 0.002) in ulcerated melanoma tumors, but not in non-ulcerated melanoma (p = 0.632, 0.416). CD2 expression also was correlated with improved OS (p = 0.021) and RFS (p = 0.001) in ulcerated melanoma, but no relationship was seen in non-ulcerated melanoma (p = 0.427, 0.682). In this small population, BRAF status did not correlate with TILs or CD2+ count.

CONCLUSION

Our data show that immune markers including TILs and CD2 count correlate more closely with survival in ulcerated melanomas than that in non-ulcerated melanomas. We propose that immune biomarkers may be particularly relevant to ulcerated, as compared to non-ulcerated, melanomas and that this merits study in larger populations.