Predicting Securities Fraud Settlements and Amounts: A Hierarchical Bayesian Model of Federal Securities Class Action Lawsuits

This article develops models that predict the incidence and amount of settlements for federal class action securities fraud litigation in the post-PLSRA period. We build hierarchical Bayesian models using data that come principally from Riskmetrics and identify several important predictors of settlement incidence (e.g., the number of different types of securities associated with a case, the company return during the class period) and settlement amount (e.g., market capitalization, measures of newsworthiness). Our models also allow us to estimate how the circuit court a case is filed in as well as the industry of the plaintiff firm associate with settlement outcomes. Finally, they allow us to accurately assess the variance of individual case outcomes revealing substantial amounts of heterogeneity in variance across cases

Predicting Securities Fraud Settlements and Amounts: A Hierarchical Bayesian Model of Federal Securities Class Action Lawsuits

This article develops models that predict the incidence and amount of settlements for federal class action securities fraud litigation in the post-PLSRA period. We build hierarchical Bayesian models using data that come principally from Riskmetrics and identify several important predictors of settlement incidence (e.g., the number of different types of securities associated with a case, the company return during the class period) and settlement amount (e.g., market capitalization, measures of newsworthiness). Our models also allow us to estimate how the circuit court a case is filed in as well as the industry of the plaintiff firm associate with settlement outcomes. Finally, they allow us to accurately assess the variance of individual case outcomes revealing substantial amounts of heterogeneity in variance across cases

A Point-Mass Mixture Random Effects Model for Pitching Metrics

A plethora of statistics have been proposed to measure the effectiveness of pitchers in Major League Baseball. While many of these are quite traditional (e.g., ERA, wins), some have gained currency only recently (e.g., WHIP, K/BB). Some of these metrics may have predictive power, but it is unclear which are the most reliable or consistent. We address this question by constructing a Bayesian random effects model that incorporates a point mass mixture and fitting it to data on twenty metrics spanning approximately 2,500 players and 35 years. Our model identifies FIP, HR/9, ERA, and BB/9 as the highest signal metrics for starters and GB%, FB%, and K/9 as the highest signal metrics for relievers. In general, the metrics identified by our model are independent of team defense. Our procedure also provides a relative ranking of metrics separately by starters and relievers and shows that these rankings differ quite substantially between them. Our methodology is compared to a Lasso-based procedure and is internally validated by detailed case studies

A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics

Numerous statistics have been proposed to measure offensive ability in Major League Baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are the most reliable or consistent. We address this issue by using a hierarchical Bayesian variable selection model to determine which offensive metrics are most predictive within players across time. Our sophisticated methodology allows for full estimation of the posterior distributions for our parameters and automatically adjusts for multiple testing, providing a distinct advantage over alternative approaches. We implement our model on a set of fifty different offensive metrics and discuss our results in the context of comparison to other variable selection techniques. We find that a large number of metrics demonstrate signal. However, these metrics are (i) highly correlated with one another, (ii) can be reduced to about five without much loss of information, and (iii) these five relate to traditional notions of performance (e.g., plate discipline, power, and ability to make contact)

A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics

Numerous statistics have been proposed to measure offensive ability in Major League Baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are the most reliable or consistent. We address this issue by using a hierarchical Bayesian variable selection model to determine which offensive metrics are most predictive within players across time. Our sophisticated methodology allows for full estimation of the posterior distributions for our parameters and automatically adjusts for multiple testing, providing a distinct advantage over alternative approaches. We implement our model on a set of fifty different offensive metrics and discuss our results in the context of comparison to other variable selection techniques. We find that a large number of metrics demonstrate signal. However, these metrics are (i) highly correlated with one another, (ii) can be reduced to about five without much loss of information, and (iii) these five relate to traditional notions of performance (e.g., plate discipline, power, and ability to make contact)

Registered replication report on Fischer, Castel, Dodd, and Pratt (2003)

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space

Predicting Securities Fraud Settlements and Amounts: A Hierarchical Bayesian Model of Federal Securities Class Action Lawsuits

This article develops models that predict the incidence and amount of settlements for federal class action securities fraud litigation in the post-PLSRA period. We build hierarchical Bayesian models using data that come principally from Riskmetrics and identify several important predictors of settlement incidence (e.g., the number of different types of securities associated with a case, the company return during the class period) and settlement amount (e.g., market capitalization, measures of newsworthiness). Our models also allow us to estimate how the circuit court a case is filed in as well as the industry of the plaintiff firm associate with settlement outcomes. Finally, they allow us to accurately assess the variance of individual case outcomes revealing substantial amounts of heterogeneity in variance across cases