Assessment of Regression Models with Discrete Outcomes Using Quasi-Empirical Residual Distribution Functions

2000 ◽

Vol 4 (1) ◽

pp. 7-16

Author(s):

Yadlin A. Marisa

Keyword(s):

Statistical Analysis ◽

Regression Models ◽

Marginal Distribution ◽

Random Variables ◽

Distribution Functions ◽

Decision Models ◽

Model Choice

The construction of J-variate distribution functions, introducing dependences among J random variables and keeping fixed the J marginal distribution functions, is important in the development of theoretical and empirical statistical analysis. Here, a method for generating such distribution functions is developed. Characteristics of the resulting distribution functions are discussed. An application to discrete regression models is presented. The latter is specialized to model choice of mode od transportation by travelers.

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A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models

PLoS ONE ◽

10.1371/journal.pone.0245627 ◽

2021 ◽

Vol 16 (1) ◽

pp. e0245627

Author(s):

Emrah Altun ◽

M. El-Morshedy ◽

M. S. Eliwa

Keyword(s):

Parameter Estimation ◽

Regression Model ◽

Regression Models ◽

Real Data ◽

Quantile Function ◽

Distribution Functions ◽

Cumulative Distribution ◽

Estimation Methods ◽

Response Variable ◽

Parameter Estimation Methods

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

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A Population-Based Model to Consider the Effect of Seasonal Variation on Serum 25(OH)D and Vitamin D Status

BioMed Research International ◽

10.1155/2015/168189 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 8

Author(s):

Philippe Vuistiner ◽

Valentin Rousson ◽

Hugues Henry ◽

Pierre Lescuyer ◽

Olivier Boulat ◽

...

Keyword(s):

Vitamin D ◽

Seasonal Variation ◽

Regression Models ◽

Population Based ◽

Distribution Functions ◽

Vitamin D Status ◽

Linear Regression Models ◽

Ultra High Pressure ◽

Swiss Population ◽

D Values

Background. We elaborated a model that predicts the centiles of the 25(OH)D distribution taking into account seasonal variation.Methods. Data from two Swiss population-based studies were used to generate (CoLaus) and validate (Bus Santé) the model. Serum 25(OH)D was measured by ultra high pressure LC-MS/MS and immunoassay. Linear regression models on square-root transformed 25(OH)D values were used to predict centiles of the 25(OH)D distribution. Distribution functions of the observations from the replication set predicted with the model were inspected to assess replication.Results. Overall, 4,912 and 2,537 Caucasians were included in original and replication sets, respectively. Mean (SD) 25(OH)D, age, BMI, and % of men were 47.5 (22.1) nmol/L, 49.8 (8.5) years, 25.6 (4.1) kg/m2, and 49.3% in the original study. The best model included gender, BMI, and sin-cos functions of measurement day. Sex- and BMI-specific 25(OH)D centile curves as a function of measurement date were generated. The model estimates any centile of the 25(OH)D distribution for given values of sex, BMI, and date and the quantile corresponding to a 25(OH)D measurement.Conclusions. We generated and validated centile curves of 25(OH)D in the general adult Caucasian population. These curves can help rank vitamin D centile independently of when 25(OH)D is measured.

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Computer processing of high-resolution images of periodic specimens

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100141834 ◽

1986 ◽

Vol 44 ◽

pp. 2-5

Author(s):

W. Chiu ◽

M.F. Schmid ◽

T.-W. Jeng

Keyword(s):

High Resolution ◽

Fourier Transforms ◽

Complex Structure ◽

Distribution Functions ◽

Multiple Image ◽

Cryo Electron Microscopy ◽

Structure Factors ◽

Unit Cells ◽

High Resolution Images ◽

Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

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