scholarly journals The Trend of Fresh Vegetables Consumption in Japan by the Maximum Marginal Likelihood Method for Smoothing Serial Data

1986 ◽  
Vol 33 (4) ◽  
pp. 238-243
Author(s):  
Masakatsu YANAGIMOTO ◽  
Naoya KUBO ◽  
Takemi YANAGIMOTO
Keyword(s):  
Marginal Likelihood ◽  
Likelihood Method ◽  
Fresh Vegetables ◽  
Serial Data ◽  
Maximum Marginal Likelihood

scholarly journals Shrinkage Parameter Estimation in Penalized Logistic Regression Analysis of Case-Control Data

2021 ◽  
Author(s):  
Ying Yu ◽  
Siyuan Chen ◽  
Brad McNeney
Keyword(s):  
Logistic Regression ◽  
Genetic Variants ◽  
Marginal Likelihood ◽  
Case Control ◽  
Likelihood Method ◽  
Case Control Studies ◽  
Rare Genetic Variants ◽  
Maximum Marginal Likelihood ◽  
Penalized Logistic Regression ◽  
Monte Carlo Em

AbstractIn genetic epidemiology, rare variant case-control studies aim to investigate the association between rare genetic variants and human diseases. Rare genetic variants lead to sparse covariates that are predominately zeros and this sparseness leads to estimators of log-OR parameters that are biased away from their null value of zero. Different penalized-likelihood methods have been developed to mitigate this sparse-data bias for case-control studies. In this research article, we study penalized logistic regression using a class of log-F priors indexed by a shrinkage parameter m to shrink the biased MLE towards zero. We propose a maximum marginal likelihood method for estimating m, with the marginal likelihood obtained by integrating the latent log-ORs out of the joint distribution of the parameters and observed data. We consider two approximate approaches to maximizing the marginal likelihood: (i) a Monte Carlo EM algorithm and (ii) a combination of a Laplace approximation and derivative-free optimization of the marginal likelihood. We evaluate the statistical properties of the estimator through simulation studies and apply the methods to the analysis of genetic data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI).

scholarly journals The Monotonic Polynomial Graded Response Model: Implementation and a Comparative Study

2020 ◽  
Vol 44 (6) ◽  
pp. 465-481
Author(s):  
Carl F. Falk
Keyword(s):  
Latent Variable ◽  
Kernel Smoothing ◽  
Marginal Likelihood ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Response Model ◽  
Response Functions ◽  
Graded Response Model ◽  
Graded Response ◽  
Maximum Marginal Likelihood

We present a monotonic polynomial graded response (GRMP) model that subsumes the unidimensional graded response model for ordered categorical responses and results in flexible category response functions. We suggest improvements in the parameterization of the polynomial underlying similar models, expand upon an underlying response variable derivation of the model, and in lieu of an overall discrimination parameter we propose an index to aid in interpreting the strength of relationship between the latent variable and underlying item responses. In applications, the GRMP is compared to two approaches: (a) a previously developed monotonic polynomial generalized partial credit (GPCMP) model; and (b) logistic and probit variants of the heteroscedastic graded response (HGR) model that we estimate using maximum marginal likelihood with the expectation–maximization algorithm. Results suggest that the GRMP can fit real data better than the GPCMP and the probit variant of the HGR, but is slightly outperformed by the logistic HGR. Two simulation studies compared the ability of the GRMP and logistic HGR to recover category response functions. While the GRMP showed some ability to recover HGR response functions and those based on kernel smoothing, the HGR was more specific in the types of response functions it could recover. In general, the GRMP and HGR make different assumptions regarding the underlying response variables, and can result in different category response function shapes.

Changepoint Analysis of Binary and Ordinal Probit Models: An Application to Bank Rate Policy Under the Interwar Gold Standard

2011 ◽  
Vol 19 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Jong Hee Park
Keyword(s):  
Time Series ◽  
Gold Standard ◽  
Time Series Data ◽  
Likelihood Function ◽  
Marginal Likelihood ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Method ◽  
Series Data ◽  
Ordinal Probit

In this paper, I introduce changepoint models for binary and ordered time series data based on Chib's hidden Markov model. The extension of the changepoint model to a binary probit model is straightforward in a Bayesian setting. However, detecting parameter breaks from ordered regression models is difficult because ordered time series data often have clustering along the break points. To address this issue, I propose an estimation method that uses the linear regression likelihood function for the sampling of hidden states of the ordinal probit changepoint model. The marginal likelihood method is used to detect the number of hidden regimes. I evaluate the performance of the introduced methods using simulated data and apply the ordinal probit changepoint model to the study of Eichengreen, Watson, and Grossman on violations of the “rules of the game” of the gold standard by the Bank of England during the interwar period.

Comparison of Uni- and Multidimensional Models Applied in Testlet-Based Tests

Methodology ◽  
2017 ◽  
Vol 13 (4) ◽  
pp. 135-143 ◽  
Author(s):  
Alejandro Hernandez-Camacho ◽  
Julio Olea ◽  
Francisco J. Abad
Keyword(s):  
Marginal Likelihood ◽  
Estimation Method ◽  
Information Criterion ◽  
Estimation Methods ◽  
Future Research ◽  
Fit Indices ◽  
Common Procedure ◽  
Item Parameters ◽  
Maximum Marginal Likelihood ◽  
Multidimensional Models

Abstract. The bifactor model (BM) and the testlet response model (TRM) are the most common multidimensional models applied to testlet-based tests. The common procedure is to estimate these models using different estimation methods (see, e.g., DeMars, 2006 ). A possible consequence of this is that previous findings about the implications of fitting a wrong model to the data may be confounded with the estimation procedures they employed. With this in mind, the present study uses the same method (maximum marginal likelihood [MML] using dimensional reduction) to compare uni- and multidimensional strategies to testlet-based tests, and assess the performance of various relative fit indices. Data were simulated under three different models, namely BM, TRM, and the unidimensional model. Recovery of item parameters, reliability estimates, and selection rates of the relative fit indices were documented. The results were essentially consistent with those obtained through different methods ( DeMars, 2006 ), indicating that the effect of the estimation method is negligible. Regarding the fit indices, Akaike Information Criterion (AIC) showed the best selection rates, whereas Bayes Information Criterion (BIC) tended to select a model which is simpler than the true one. The work concludes with recommendations for practitioners and proposals for future research.

Modeling Nonignorable Missing Data in Speeded Tests

2008 ◽  
Vol 68 (6) ◽  
pp. 907-922 ◽  
Author(s):  
Cees A. W. Glas ◽  
Jonald L. Pimentel
Keyword(s):  
Missing Data ◽  
Marginal Likelihood ◽  
Distribution Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Missing Responses ◽  
Item Parameters ◽  
Maximum Marginal Likelihood ◽  
Nonignorable Missing ◽  
Linear Restrictions

In tests with time limits, items at the end are often not reached. Usually, the pattern of missing responses depends on the ability level of the respondents; therefore, missing data are not ignorable in statistical inference. This study models data using a combination of two item response theory (IRT) models: one for the observed response data and one for the missing data indicator. The missing data indicator is modeled using a sequential model with linear restrictions on the item parameters. The models are connected by the assumption that the respondents' latent proficiency parameters have a joint multivariate normal distribution. Model parameters are estimated by maximum marginal likelihood. Simulations show that treating missing data as ignorable can lead to considerable bias in parameter estimates. Including an IRT model for the missing data indicator removes this bias. The method is illustrated with data from an intelligence test with a time limit.

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