Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function

Biometrika ◽  
2003 ◽  
Vol 90 (4) ◽  
pp. 765-775 ◽  
Author(s):  
Z. Wang
Keyword(s):  
Distribution Function ◽  
Random Intercept ◽  
Bridge Distribution

scholarly journals Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Payam Amini ◽  
Abbas Moghimbeigi ◽  
Farid Zayeri ◽  
Leili Tapak ◽  
Saman Maroufizadeh ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Normal Distribution ◽  
Ordinal Logistic Regression ◽  
Accurate Estimation ◽  
Joint Modelling ◽  
Random Intercept ◽  
Bridge Distribution ◽  
Response Variables ◽  
Normally Distributed ◽  
Ordinal Outcome

Associated longitudinal response variables are faced with variations caused by repeated measurements over time along with the association between the responses. To model a longitudinal ordinal outcome using generalized linear mixed models, integrating over a normally distributed random intercept in the proportional odds ordinal logistic regression does not yield a closed form. In this paper, we combined a longitudinal count and an ordinal response variable with Bridge distribution for the random intercept in the ordinal logistic regression submodel. We compared the results to that of a normal distribution. The two associated response variables are combined using correlated random intercepts. The random intercept in the count outcome submodel follows a normal distribution. The random intercept in the ordinal outcome submodel follows Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modelling approaches. To illustrate the performance of the model, a simulation study was conducted. Based on the simulation results, assuming a Bridge distribution for the random intercept of ordinal logistic regression results in accurate estimation even if the random intercept is normally distributed. Moreover, considering the association between longitudinal count and ordinal responses resulted in estimation with lower standard error in comparison to univariate analysis. In addition to the same interpretation for the parameter in marginal and conditional estimates thanks to the assumption of a Bridge distribution for the random intercept of ordinal logistic regression, more efficient estimates were found compared to that of normal distribution.

From Bi-Dimensionality to Uni-Dimensionality in Self-Report Questionnaires

2020 ◽  
pp. 1-14 ◽  
Author(s):  
Bjarne Schmalbach ◽  
Markus Zenger ◽  
Michalis P. Michaelides ◽  
Karin Schermelleh-Engel ◽  
Andreas Hinz ◽  
...  
Keyword(s):  
Factor Model ◽  
Common Factor ◽  
Self Regulation ◽  
Model Fit ◽  
Self Report ◽  
External Criterion ◽  
Common Factor Model ◽  
Random Intercept ◽  
Using Data ◽  
Core Self

Abstract. The common factor model – by far the most widely used model for factor analysis – assumes equal item intercepts across respondents. Due to idiosyncratic ways of understanding and answering items of a questionnaire, this assumption is often violated, leading to an underestimation of model fit. Maydeu-Olivares and Coffman (2006) suggested the introduction of a random intercept into the model to address this concern. The present study applies this method to six established instruments (measuring depression, procrastination, optimism, self-esteem, core self-evaluations, and self-regulation) with ambiguous factor structures, using data from representative general population samples. In testing and comparing three alternative factor models (one-factor model, two-factor model, and one-factor model with a random intercept) and analyzing differential correlational patterns with an external criterion, we empirically demonstrate the random intercept model’s merit, and clarify the factor structure for the above-mentioned questionnaires. In sum, we recommend the random intercept model for cases in which acquiescence is suspected to affect response behavior.

Influence of extinction phenomenon on determination of the orientation distribution function

2006 ◽  
Vol 2006 (suppl_23_2006) ◽  
pp. 175-180
Author(s):  
G. Gómez-Gasga ◽  
T. Kryshtab ◽  
J. Palacios-Gómez ◽  
A. de Ita de la Torre
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Orientation Distribution

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

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