scholarly journals Categorical Omega With Small Sample Sizes via Bayesian Estimation: An Alternative to Frequentist Estimators

2018 ◽  
Vol 79 (1) ◽  
pp. 19-39 ◽  
Author(s):  
Yanyun Yang ◽  
Yan Xia
Keyword(s):  
Least Squares ◽  
Bayesian Estimation ◽  
Weighted Least Squares ◽  
Small Sample ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Diagonally Weighted Least Squares

When item scores are ordered categorical, categorical omega can be computed based on the parameter estimates from a factor analysis model using frequentist estimators such as diagonally weighted least squares. When the sample size is relatively small and thresholds are different across items, using diagonally weighted least squares can yield a substantially biased estimate of categorical omega. In this study, we applied Bayesian estimation methods for computing categorical omega. The simulation study investigated the performance of categorical omega under a variety of conditions through manipulating the scale length, number of response categories, distributions of the categorical variable, heterogeneities of thresholds across items, and prior distributions for model parameters. The Bayes estimator appears to be a promising method for estimating categorical omega. M plus and SAS codes for computing categorical omega were provided.

scholarly journals On the Burr XII-moment exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246935
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Wenhui Sheng ◽  
Azeem Ali
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simulation Studies ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications.

Comparison of Alternative Estimation Methods in Confirmatory Factor Analyses of the General Health Questionnaire

2005 ◽  
Vol 97 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Wei C. Wang ◽  
Everarda G. Cunningham
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
General Health Questionnaire ◽  
Estimation Methods ◽  
Health Questionnaire ◽  
Factor Analyses ◽  
Confirmatory Factor Analyses ◽  
Weighted Least Squares Estimation ◽  
Confirmatory Factor ◽  
Diagonally Weighted Least Squares

This paper examines the implications of violating assumptions concerning the continuity and distributional properties of data in establishing measurement models in social science research. The General Health Questionnaire-12 uses an ordinal response scale. Responses to the GHQ-12 from 201 Hong Kong immigrants on arrival in Australia showed that the data were not normally distributed. A series of confirmatory factor analyses using either a Pearson product-moment or a polychoric correlation input matrix and employing either maximum likelihood, weighted least squares or diagonally weighted least squares estimation methods were conducted on the data. The parameter estimates and goodness-of-fit statistics provided support for using polychoric correlations and diagonally weighted least squares estimation when analyzing ordinal, nonnormal data.

scholarly journals A New Three-Parameter Exponential Distribution with Variable Shapes for the Hazard Rate: Estimation and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 135 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Osama Abdo Mohamed
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Mathematical Properties ◽  
Anderson Darling ◽  
Von Mises

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates, and right-skewed, left-skewed, symmetrical, and reversed-J shaped densities. Some mathematical properties of the proposed distribution are derived. The model parameters are estimated via eight frequentist estimation methods called, the maximum likelihood estimators, least squares and weighted least-squares estimators, maximum product of spacing estimators, Cramér-von Mises estimators, percentiles estimators, and Anderson-Darling and right-tail Anderson-Darling estimators. Extensive simulations are conducted to compare the performance of these estimation methods for small and large samples. Four practical data sets from the fields of medicine, engineering, and reliability are analyzed, proving the usefulness and flexibility of the proposed distribution.

scholarly journals The Effect of Estimation Methods on SEM Fit Indices

2019 ◽  
Vol 80 (3) ◽  
pp. 421-445 ◽  
Author(s):  
Dexin Shi ◽  
Alberto Maydeu-Olivares
Keyword(s):  
Least Squares ◽  
Root Mean Square ◽  
Structural Equation ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Estimation Methods ◽  
Equation Modeling ◽  
Model Parameters ◽  
Mean Square ◽  
Fit Indices

We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). We considered different types and levels of misspecification in factor analysis models: misspecified dimensionality, omitting cross-loadings, and ignoring residual correlations. Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators. In contrast, SRMR is robust to the method used to estimate the model parameters. The same criterion can be applied at the population level when using the SRMR to evaluate model fit, regardless of the choice of estimation method.

scholarly journals The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1684 ◽  
Author(s):  
Maha A. D. Aldahlan ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Finite Sample ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

scholarly journals The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2060
Author(s):  
Mashail M. AL Sobhi
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Inverse Power ◽  
Model Parameters ◽  
Proposed Model ◽  
Anderson Darling ◽  
Von Mises ◽  
Insurance Data

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

scholarly journals Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Muhammad Ahsan ul Haq ◽  
Sharqa Hashmi ◽  
Mahmoud Elsehety
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Quantile Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Alpha Power ◽  
Lomax Distribution ◽  
Anderson Darling ◽  
Inverse Lomax Distribution

In this paper, a new three-parameter lifetime distribution, alpha power transformed inverse Lomax (APTIL) distribution, is proposed. The APTIL distribution is more flexible than inverse Lomax distribution. We derived some mathematical properties including moments, moment generating function, quantile function, mode, stress strength reliability, and order statistics. Characterization related to hazard rate function is also derived. The model parameters are estimated using eight estimation methods including maximum likelihood, least squares, weighted least squares, percentile, Cramer–von Mises, maximum product of spacing, Anderson–Darling, and right-tail Anderson–Darling. Numerical results are calculated to compare the performance of these estimation methods. Finally, we used three real-life datasets to show the flexibility of the APTIL distribution.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

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