Search Results (6)

As life expectancy increases, pension plans face growing longevity risk. Standardized longevity-linked securities such as survivor contracts allow pension plans to transfer this risk to capital markets. However, more consensus is needed on the appropriate mortality model and premium principle to price these contracts. This paper investigates the impact of the mortality model and premium principle choice on the pricing, risk measurement, and modeling of survivor contracts. We present a framework for evaluating risk measures associated with survivor contracts, specifically survivor forwards (S-forward) and survivor swaps (S-swaps). We analyze how the mortality model and premium principle assumptions affect pricing and risk measures (value-at-risk and expected shortfall). Four mortality models (Lee–Carter, Renshaw–Haberman, Cairns–Blake–Dowd, and M6) and eight premium principles (Wang, proportional hazard, dual power, Gini, exponential, standard deviation, variance, and median absolute deviation) are considered. Our analysis highlights the need to refine mortality models and premium principles to enhance pricing accuracy and risk management. We also suggest regulators and practitioners incorporate expected shortfall alongside value-at-risk to capture tail risks and improve capital allocation. Full article

Haberman linking is a widely used method for comparing groups using the two-parameter logistic item response model. However, the traditional Haberman linking approach relies on joint item parameter estimation, which prevents the application of standard M-estimation theory for linking error calculation in the presence of differential item functioning. To address this limitation, a novel pairwise Haberman linking method is introduced. Pairwise Haberman linking aligns with Haberman linking when no items are missing but eliminates the need for joint item parameters, allowing for the use of M-estimation theory in linking error computation. Theoretical derivations and simulation studies show that pairwise Haberman linking delivers reliable statistical inferences for items and persons, particularly in terms of coverage rates. Furthermore, using a bias-corrected linking error is recommended to reduce the influence of sample size on error estimates. Full article

Linking methods are widely used in the social sciences to compare group differences regarding the mean and the standard deviation of a factor variable. This article examines a comparison between robust Haberman linking (HL) and invariance alignment (IA) for factor models with dichotomous and continuous items, utilizing the $L_{0.5}$ and $L_0$ loss functions. A simulation study demonstrates that HL outperforms IA when item intercepts are used for linking, rather than the original HL approach, which relies on item difficulties. The results regarding the choice of loss function were mixed: $L_0$ showed superior performance in the simulation study with continuous items, while $L_{0.5}$ performed better in the study with dichotomous items. Full article

Mean-geometric mean (MGM) linking is a widely used method for linking two groups within the two-parameter logistic (2PL) item response model. However, the presence of differential item functioning (DIF) can lead to biased parameter estimates using the traditional MGM method. To address this, alternative linking methods based on robust loss functions have been proposed. In this article, the conventional $L_2$ loss function is compared with the $L_{0.5}$ and $L_0$ loss functions in MGM linking. Our results suggest that robust loss functions are preferable when dealing with outlying DIF effects, with the $L_0$ function showing particular advantages in tests with larger item sets and sample sizes. Additionally, a simulation study demonstrates that defining MGM linking based on item intercepts rather than item difficulties leads to more accurate linking parameter estimates. Finally, robust Haberman linking slightly outperforms robust MGM linking in two-group comparisons. Full article

This article investigates the comparison of two groups based on the two-parameter logistic item response model. It is assumed that there is random differential item functioning in item difficulties and item discriminations. The group difference is estimated using separate calibration with subsequent linking, as well as concurrent calibration. The following linking methods are compared: mean-mean linking, log-mean-mean linking, invariance alignment, Haberman linking, asymmetric and symmetric Haebara linking, different recalibration linking methods, anchored item parameters, and concurrent calibration. It is analytically shown that log-mean-mean linking and mean-mean linking provide consistent estimates if random DIF effects have zero means. The performance of the linking methods was evaluated through a simulation study. It turned out that (log-)mean-mean and Haberman linking performed best, followed by symmetric Haebara linking and a newly proposed recalibration linking method. Interestingly, linking methods frequently found in applications (i.e., asymmetric Haebara linking, recalibration linking used in a variant in current large-scale assessment studies, anchored item parameters, concurrent calibration) perform worse in the presence of random differential item functioning. In line with the previous literature, differences between linking methods turned out be negligible in the absence of random differential item functioning. The different linking methods were also applied in an empirical example that performed a linking of PISA 2006 to PISA 2009 for Austrian students. This application showed that estimated trends in the means and standard deviations depended on the chosen linking method and the employed item response model. Full article

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses an extension of invariance alignment and Haberman linking by choosing the robust power loss function $\rho \left(x\right)={\left|x\right|}^p$$(p>0)$. This power loss function with power values p smaller than one is particularly suited for item responses that are generated under partial invariance. For a general class of linking functions, asymptotic normality of estimates is shown. Moreover, the theory of M-estimation is applied for obtaining linking errors (i.e., inference with respect to a population of items) for this class of linking functions. In a simulation study, it is shown that invariance alignment and Haberman linking have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment. In three examples, the influence of the choice of a particular linking function on the estimation of group means is demonstrated. It is concluded that the choice of the loss function in linking is related to structural assumptions about the pattern of noninvariance in item parameters. Full article