Linear latent structure analysis: Mixture distribution models with linear constraints

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the local independence assumption. LLS analysis explicitly considers a family of mixed distributions as a linear space, and LLS models are obtained by imposing linear constraints on the mixing distribution.LLS models are identifiable under modest conditions and are consistently estimable. A remarkable feature of LLS analysis is the existence of a high-performance numerical algorithm, which reduces parameter estimation to a sequence of linear algebra problems. Simulation experiments with a prototype of the algorithm demonstrated a good quality of restoration of model parameters.     

Reducing Risk on Machinery: A Field Evaluation Pilot Study of Risk Assessment

A pilot evaluation of the ANSI B11-TR3 Machinery Risk Assessment/Risk Reduction (RA/RR) Guideline was conducted. The TR3 guideline was introduced into five companies on one machinery system in each company with a second machine system serving as a control. A pre-post investigation was performed with safety conditions measured pre and post in both treatment and control and with risk reduction score measured only in the treatment machine system. NIOSH provided a commercially available risk assessment software to facilitate the process. Evaluation measures included avoided injuries, reduced exposure to machinery hazards, pretest and posttest knowledge demonstration, assessment of group processes following training, correct implementation of the guidelines, and degree to which risk reduction recommendations were implemented. The qualitative results of this pilot effort appear to be the best indicators for the way ahead in industrial machine risk assessment. All companies indicated that they derived value in participating in this study and in conducting risk assessments. Quantitative study results suggest that: (1) as measured by the knowledge of the participants before and after the TR3 training, the guidelines can be effective at enhancing employee knowledge of safe machine operations and (2) although the injury reduction trends appear successful, the small sample size in the study size should be considered in interpreting these early results.     

Economic Pressure, Maternal Depression, and Child Adjustment in Latino Families: An Exploratory Study

The goal of this study was to investigate the impact of poverty and economic pressure upon the adjustment of mothers and children in immigrant Latino families. Participants included 56 first generation Latina mothers who completed questionnaires addressing economic difficulties, depression, social support, and behavior problems exhibited by their children (30 boys, 26 girls) who ranged in ages from 4 to 13. Results indicate that maternal depression mediates the relationship between maternal economic pressure and child adjustment. Social support was found to further moderate the relationship between maternal depression and child internalizing problems. Gender differences indicated that relations were stronger among mothers of boys than mothers of girls.     

Equating Poisson and Normal Probability Functions to Derive Stirling's Formula

Often texts for introductory courses in probability or mathematical statistics make reference to Stirling's asymptotic formula (for a factorial) without presenting any proof or justification for the formula. A notable exception is Feller. In this article, we present a derivation of Stirling's formula based on the normal approximation of a Poisson probability that is considerably more accessible to the average student than Feller's approach. Besides illustrating a usage of the central limit theorem in conjunction with a continuity correction, the derivation lends itself to a mnemonic device for quickly obtaining Stirling's formula.     

The Use of Multizone Models to Estimate an Airborne Chemical Contaminant Generation and Decay Profile: Occupational Exposures of Hairdressers to Vinyl Chloride in Hairspray During the 1960s and 1970s

Vinyl chloride (VC) was used as a propellant in a limited percentage of aerosol hairspray products in the United States from approximately 1967 to 1973. The question has arisen whether occupational exposures of hairdressers to VC-containing hairsprays in hair salons were sufficient to increase the risk for developing hepatic angiosarcoma (HAS). Transient two-zone and steady-state three-zone models were used to estimate the historical airborne concentration of VC for individual hairdressers using hairspray as well as estimated contributions from other hairdressers in the same salon. Concentrations of VC were modeled for small, medium, and large salons, as well as a representative home salon. Model inputs were determined using published literature, and variability in these inputs was also considered using Monte Carlo techniques. The 95th percentile for the daily time-weighted average exposure for small, medium, and large salons, assuming a market-share fraction of VC-containing hairspray use from the Monte Carlo analysis, was about 0.3 ppm, and for the home salon scenario was 0.1 ppm. The 95th percentile value for the cumulative lifetime exposure of the hairdressers was 2.8 ppm-years for the home salon scenario and 2.0 ppm-years for the small, medium, and large salon scenarios. If using the assumption that all hairsprays used in a salon contained VC, the 95th percentile of the theoretical lifetime cumulative dose was estimated to be 52–79 ppm-years. Estimated lifetime doses were all below the threshold dose for HAS of about 300 to 500 ppm-years reported in the published epidemiology literature.     

AN EARLY START: Skill Grouping and Unequal Reading Gains in the Elementary Years

Separating elementary school students into skill-based reading groups within classrooms affects a vast majority of young children in the United States. The impact of this institutional process on students' learning has important implications for sociological perspectives on education and stratification, yet a lack of studies comparing similar grouped and nongrouped students has prevented scholars from drawing conclusions as to the salience of this type of curriculum differentiation. Drawing on data from the first- and third-grade waves of the Early Childhood Longitudinal Study-Kindergarten Cohort, I use propensity score matching techniques to estimate the impact of low, middle, and high group placement on reading gains relative to nongrouped instruction. Findings suggest that high-grouped students learn more, and low-grouped students learn less, than comparable nongrouped students. These analyses, which significantly lessen the extent to which selection into groups may bias results, add strong evidence to the view that within-classroom skill grouping in the early elementary years promotes unequal reading gains compared to nongrouped instruction. I conclude by discussing the theoretical and policy implications of these findings.