Full Maximum Likelihood Method Research Articles

On The Estimation Of The Shape Parameter Of A Symmetric Distribution

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1/���� portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.

On the Estimation of the Shape Parameter of a Symmetric Distribution

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1-1/n portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.

A Comparison of Factor Score Estimation Methods in the Presence of Missing Data: Reliability and an Application to Nicotine Dependence

Factor score estimation is a controversial topic in psychometrics, and the estimation of factor scores from exploratory factor models has historically received a great deal of attention. However, both confirmatory factor models and the existence of missing data have generally been ignored in this debate. This article presents a simulation study that compares the reliability of sum scores, regression-based and expected posterior methods for factor score estimation for confirmatory factor models in the presence of missing data. Although all methods perform reasonably well with complete data, expected posterior-weighted (full) maximum likelihood methods are significantly more reliable than sum scores and regression estimators in the presence of missing data. Factor score reliability for complete data can be predicted by Guttman's 1955 formula for factor communality. Furthermore, factor score reliability for incomplete data can be reasonably approximated by communality raised to the power. An empirical demonstration shows that the full maximum likelihood method best preserves the relationship between nicotine dependence and a genetic predictor under missing data. Implications and recommendations for applied research are discussed.

Multivariate Latent Growth Models for Mixed Data with Covariate Effects

The paper presents an extension of a new class of multivariate latent growth models (Bianconcini and Cagnone, 2012) to allow for covariate effects on manifest, latent variables and random effects. The new class of models combines: (i) multivariate latent curves that describe the temporal behavior of the responses, and (ii) a factor model that specifies the relationship between manifest and latent variables. Based on the Generalized Linear and Latent Variable Model framework (Bartholomew and Knott, 1999), the response variables are assumed to follow different distributions of the exponential family, with item-specific linear predictors depending on both latent variables and measurement errors. A full maximum likelihood method is used to estimate all the model parameters simultaneously. Data coming from the Data WareHouse of the University of Bologna are used to illustrate the methodology.

Comparison of estimators in nested case–control studies with multiple outcomes

Reuse of controls in a nested case-control (NCC) study has not been considered feasible since the controls are matched to their respective cases. However, in the last decade or so, methods have been developed that break the matching and allow for analyses where the controls are no longer tied to their cases. These methods can be divided into two groups; weighted partial likelihood (WPL) methods and full maximum likelihood methods. The weights in the WPL can be estimated in different ways and four estimation procedures are discussed. In addition, we address modifications needed to accommodate left truncation. A full likelihood approach is also presented and we suggest an aggregation technique to decrease the computation time. Furthermore, we generalize calibration for case-cohort designs to NCC studies. We consider a competing risks situation and compare WPL, full likelihood and calibration through simulations and analyses on a real data example.

Within-woman change in regulatory T cells from pregnancy to the postpartum period

Regulatory T cells (Treg cells) are an important area of investigation in human health and disease. In this study, the trajectory of percentage of Treg cells (defined as CD4+CD25+Foxp3+CD127--lymphocytes) was measured in the blood of 208 women during pregnancy and up to three additional times in the postpartum period (1, 6 and 12 months postpartum). Whether the trajectory was affected by gravidity, parity, neonatal sex, pet exposure, maternal atopic and asthma status, smoking, maternal race or other pregnancy factors was examined. Multilevel models were fit using full maximum likelihood methods and included both random and fixed effects. Overall, percentages of Treg cells increased from the prenatal to the postpartum period. Among women who were not atopic, nulliparous women had lower percentages of Treg cells over time compared with parous women. Atopic women with pets in the home during pregnancy had lower percentages of Treg cells than atopic women who did not have pets. The trajectory was not affected by the other factors investigated. We conclude that within-woman change in percentages of Treg cells may vary by time in relation to delivery, as well as by maternal atopic status and exposure to pets and number of prior births. The data did not indicate an overall decline in Treg cells in the postpartum period. Future work to better identify the role of Treg cells in successful pregnancy would ideally include a set of well characterized women sampled serially starting prior to pregnancy and throughout the postpartum period.

Meta-Analysis of the Relative Efficiency of Methionine-Hydroxy-Analogue-Free-Acid Compared with dl-Methionine in Broilers Using Nonlinear Mixed Models

The purpose of this paper was to perform a meta-analysis to compare the biological efficiency of dl-methionine with methionine-hydroxy-analogue-free-acid in broiler chickens. A database was developed which contained dose-response studies of these 2 methionine sources. Criteria for entry into the database were defined before the meta-analysis was initiated. Data from 46 dose-response experiments, extracted from a total of 27 peer-reviewed papers, were used for the analysis with the Statistical Analysis System. Initially, the NLIN procedure was applied to fit an exponential model of the form y = α + β*[1 − exp (−γ *dose)] + e. Thereafter, meta-analysis was conducted by means of nonlinear mixed models, which were fitted by a full maximum likelihood method as implemented in the NLMIXED procedure. The nonlinear model used for the analysis allowed for separate plateaus or different efficiencies of the methionine sources. Mixed modeling was applied to account for heterogeneity among the studies in all regression parameters for both sources of methionine via random effects. Statistical hypotheses were tested by the asymptotic Wald test. In addition, potential co-variables were tested for inclusion as linear regressors for the nonlinear model parameters. In conclusion, the null hypothesis of equal plateaus of the 2 methionine sources was not rejected. The analyses of the response variables average daily gain (ADG) and gain to feed ratio (GF) showed a highly significant difference between the tested methionine sources. The covariate age at start of experiment significantly affected the intercept term α for the response variables ADG and GF, respectively. The meta-analysis showed that biological efficiencies of dl-methionine-hydroxy-analogue-free-acid were 81 and 79% of the values for dl-methionine, on an equimolar basis, for ADG and GF, respectively.

Full Maximum Likelihood Estimation of Polychoric and Polyserial Correlations With Missing Data

This article develops a full maximum likelihood method for obtaining joint estimates of variances and correlations among continuous and polytomous variables with incomplete data which are missing at random with an ignorable missing mechanism. The approach for obtaining the maximum likelihood estimate of the covariance matrix is via a simple confirmatory analysis model with a fixed identity loading matrix and a fixed diagonal matrix with small of unique variances. A Monte Carlo Expectation-Maximization (MCEM) algorithm is constructed to obtain the solution, in which the E-step is approximated by observations simulated by the Gibbs sampler. Results from a simulation study and a real example are provided to illustrate the methodology.

Kinetic behavior of cloned mouse acetylcholine receptors. A semi-autonomous, stepwise model of gating

This model assumes that any conformational changes consequent to binding one ligand are kinetically undetectable (on the time scale of the instrumentation) and/or irrelevant to the gating process. We have analysed AChR activation kinetics according to an alternative scheme that explicitly incorporates agonist-induced conformational changes. In this stepwise model, each subunit undergoes an isomerization after binding an agonist, with ionic conduction occurring only after both subunits have activated: -100 mV). Kinetic analysis followed the Horn and Lange (1983) full maximum likelihood method, with a first-order correction for missed events (Roux and Sauve, 1985). After selecting a subset of bursts that was apparently homogeneous, the rates of either activation scheme were iteratively adjusted by a Simplex algorithm until the -log likelihood was a minimum. The significance of the log likelihood ratios (LLR) was examined both by resampling and simulation methods (Horn, 1987). At 1,000 ~M, the predominant component of gaps with bursts has a time constant of 64 ~s, indicating an effective opening rate at this concentration of 15,600 S-I. The results of the likelihood fit to a patch exposed to 10 ~M ACh are shown below (all rates are S-I or S-l ~M-l). The association and dissociation rates of the stepwise scheme were assumed to be equal and independent, so that each model had the same number of independent parameters (six).