Equating Oral Reading Fluency Scores: A Model-Based Approach.

Words read correctly per minute (WCPM) is the reporting score metric in oral reading fluency (ORF) assessments, which is popularly utilized as part of curriculum-based measurements to screen at-risk readers and to monitor progress of students who receive interventions. Just like other types of assessments with multiple forms, equating would be necessary when WCPM scores are obtained from multiple ORF passages to be compared both between and within students. This article proposes a model-based approach for equating WCPM scores. A simulation study was conducted to evaluate the performance of the model-based equating approach along with some observed-score equating methods with external anchor test design.

Penalized likelihood methods for modeling count data.

The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during the assessment of oral reading fluency (ORF) in school-aged children. A sample of fourth-grade students were given one of ten available passages to read with these differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. Two types of penalty functions are considered for penalized likelihood with respective goals of shrinking parameter estimates closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as metric. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The paper concludes with an analysis of the motivating ORF data.

Density estimation in the presence of heteroscedastic measurement error of unknown type using phase function deconvolution.

It is important to properly correct for measurement error when estimating density functions associated with biomedical variables. These estimators that adjust for measurement error are broadly referred to as density deconvolution estimators. While most methods in the literature assume the distribution of the measurement error to be fully known, a recently proposed method based on the empirical phase function (EPF) can deal with the situation when the measurement error distribution is unknown. The EPF density estimator has only been considered in the context of additive and homoscedastic measurement error; however, the measurement error of many biomedical variables is heteroscedastic in nature. In this paper, we developed a phase function approach for density deconvolution when the measurement error has unknown distribution and is heteroscedastic. A weighted EPF (WEPF) is proposed where the weights are used to adjust for heteroscedasticity of measurement error. The asymptotic properties of the WEPF estimator are evaluated. Simulation results show that the weighting can result in large decreases in mean integrated squared error when estimating the phase function. The estimation of the weights from replicate observations is also discussed. Finally, the construction of a deconvolution density estimator using the WEPF is compared with an existing deconvolution estimator that adjusts for heteroscedasticity but assumes the measurement error distribution to be fully known. The WEPF estimator proves to be competitive, especially when considering that it relies on minimal assumption of the distribution of measurement error.

Moment reconstruction and moment-adjusted imputation when exposure is generated by a complex, nonlinear random effects modeling process.

For the classical, homoscedastic measurement error model, moment reconstruction (Freedman et al., 2004, 2008) and moment-adjusted imputation (Thomas et al., 2011) are appealing, computationally simple imputation-like methods for general model fitting. Like classical regression calibration, the idea is to replace the unobserved variable subject to measurement error with a proxy that can be used in a variety of analyses. Moment reconstruction and moment-adjusted imputation differ from regression calibration in that they attempt to match multiple features of the latent variable, and also to match some of the latent variable's relationships with the response and additional covariates. In this note, we consider a problem where true exposure is generated by a complex, nonlinear random effects modeling process, and develop analogues of moment reconstruction and moment-adjusted imputation for this case. This general model includes classical measurement errors, Berkson measurement errors, mixtures of Berkson and classical errors and problems that are not measurement error problems, but also cases where the data-generating process for true exposure is a complex, nonlinear random effects modeling process. The methods are illustrated using the National Institutes of Health-AARP Diet and Health Study where the latent variable is a dietary pattern score called the Healthy Eating Index-2005. We also show how our general model includes methods used in radiation epidemiology as a special case. Simulations are used to illustrate the methods.