scholarly journals BAYESIAN SIMULTANEOUS EQUATIONS ANALYSIS USING REDUCED RANK STRUCTURES

1998 ◽  
Vol 14 (6) ◽  
pp. 701-743 ◽  
Author(s):  
Frank Kleibergen ◽  
Herman K. van Dijk
Keyword(s):  
Linear Model ◽  
Structural Equation ◽  
Linear Models ◽  
A Priori ◽  
Simultaneous Equation ◽  
Reduced Form ◽  
Bayesian Analyses ◽  
Reduced Rank ◽  
Rank Restrictions ◽  
Standard Linear

Diffuse priors lead to pathological posterior behavior when used in Bayesian analyses of simultaneous equation models (SEM's). This results from the local nonidentification of certain parameters in SEM's. When this a priori known feature is not captured appropriately, it results in an a posteriori favoring of certain specific parameter values that is not the consequence of strong data information but of local nonidentification. We show that a proper consistent Bayesian analysis of a SEM explicitly has to consider the reduced form of the SEM as a standard linear model on which nonlinear (reduced rank) restrictions are imposed, which result from a singular value decomposition. The priors/posteriors of the parameters of the SEM are therefore proportional to the priors/posteriors of the parameters of the linear model under the condition that the restrictions hold. This leads to a framework for constructing priors and posteriors for the parameters of SEM's. The framework is used to construct priors and posteriors for one, two, and three structural equation SEM's. These examples together with a theorem, showing that the reduced forms of SEM's accord with sets of reduced rank restrictions on standard linear models, show how Bayesian analyses of generally specified SEM's can be conducted.

scholarly journals ADMISSIBLE SIGNIFICANCE TESTS IN SIMULTANEOUS EQUATION MODELS

2017 ◽  
Vol 33 (3) ◽  
pp. 534-550
Author(s):  
Theodore W. Anderson
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Structural Equation ◽  
Alternative Hypothesis ◽  
Simultaneous Equation ◽  
Reduced Form ◽  
Ratio Test ◽  
Linear Transformations ◽  
Significance Level ◽  
Endogenous Variables

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the disturbance covariance matrix is known, it can be set to the identity, and the invariance of the endogenous variables is with respect to orthogonal transformations. The likelihood ratio test is invariant with respect to these transformations and is the best invariant test. Furthermore it is admissible in the class of all tests. Any other test has lower power and/or higher significance level. In particular, this likelihood ratio test dominates a test based on the Two-Stage Least Squares estimator.

scholarly journals Two seemingly paradoxical results in linear models: the variance inflation factor and the analysis of covariance

2021 ◽  
Vol 9 (1) ◽  
pp. 1-8
Author(s):  
Peng Ding
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Ordinary Least Squares ◽  
Analysis Of Covariance ◽  
Variance Inflation Factor ◽  
Standard Linear ◽  
Inflation Factor ◽  
Effect Estimation ◽  
The Cost ◽  
Paradoxical Results

Abstract A result from a standard linear model course is that the variance of the ordinary least squares (OLS) coefficient of a variable will never decrease when including additional covariates into the regression. The variance inflation factor (VIF) measures the increase of the variance. Another result from a standard linear model or experimental design course is that including additional covariates in a linear model of the outcome on the treatment indicator will never increase the variance of the OLS coefficient of the treatment at least asymptotically. This technique is called the analysis of covariance (ANCOVA), which is often used to improve the efficiency of treatment effect estimation. So we have two paradoxical results: adding covariates never decreases the variance in the first result but never increases the variance in the second result. In fact, these two results are derived under different assumptions. More precisely, the VIF result conditions on the treatment indicators but the ANCOVA result averages over them. Comparing the estimators with and without adjusting for additional covariates in a completely randomized experiment, I show that the former has smaller variance averaging over the treatment indicators, and the latter has smaller variance at the cost of a larger bias conditioning on the treatment indicators. Therefore, there is no real paradox.

Comparison of models using different censoring scenarios for days open in Spanish Holstein cows

2006 ◽  
Vol 82 (2) ◽  
pp. 233-239 ◽  
Author(s):  
O. González-Recio ◽  
Y.M. Chang ◽  
D. Gianola ◽  
K. A. Weigel
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Post Partum ◽  
Open Data ◽  
Rank Correlation ◽  
Predictive Ability ◽  
Logarithmic Scale ◽  
Data Set ◽  
Standard Linear ◽  
Days Open

AbstractDays open data from 113 569 lactation records in 774 Spanish Holstein herds were analysed using standard linear models under two different editing procedures, and with two alternative methodologies that account for censoring: a censored linear model (CLM) and a Weibull survival analysis (SA) model. The first editing procedure excluded from the linear model all censored records for days open (LMnc), and the second defined days open as days from calving to the last known insemination or culling date, treating censored records as complete (LM). Sire variance estimates for days open were 61, 70 and 139 for LMnc, LM and CLM, respectively, and 0·026 for SA on a logarithmic scale. Heritability estimates were 0·05, 0·06 and 0·08 with LMnc, LM and CLM, respectively. Rankings of sires varied between methodologies: sire evaluations from LMnc and LM had rank correlations with evaluations from SA equal to −0·65 and −0·82, respectively, and of 0·71 and 0·87 with evaluations from CLM. The rank correlation between evaluations from SA and CLM was −0·98, suggesting stronger agreement of sire rankings between models that take censoring into account.The SA model had a better predictive ability of daughter fertility at early stages of lactation than the other methods, as measured by chi-squared statistics for predicted pregnancy status at 75, 103, 140, or 200 days post partum in a split data set. The CLM also predicted daughter fertility more accurately than any of the two standard linear models.

scholarly journals ESTIMASI PARAMETER PADA SISTEM MODEL PERSAMAAN SIMULTAN DATA PANEL DINAMIS DENGAN METODE 2 SLS GMM-AB

2018 ◽  
Vol 11 (2) ◽  
pp. 79-91
Author(s):  
Arya Fendha Ibnu Shina
Keyword(s):  
Panel Data ◽  
Structural Equation ◽  
Simultaneous Equation ◽  
Equation Model ◽  
Dynamic Panel Data ◽  
Least Square ◽  
System Model ◽  
Reduced Form ◽  
Simultaneous Equation Model ◽  
Dynamic Panel

Single equation models ignore interdependencies or two-way relationships between response variables. The simultaneous equation model accommodates this two-way relationship form. Two Stage Least Square Generalized Methods of Moment Arellano and Bond (2 SLS GMM-AB) is used to estimate the parameters in the simultaneous system model of dynamic panel data if each structural equation is exactly identified or over identified. In the simultaneous equation system model with dynamic panel data, each structural equation and reduced form is a dynamic panel data regression equation. Estimation of structural equations and reduced form using Ordinary Least Square (OLS) resulted biased and inconsistent estimators. Arellano and Bond GMM method (GMM AB) estimator produces unbiased, consistent, and efficient estimators.The purpose of this paper is to explain the steps of 2 SLS GMM-AB method to estimate parameter in simultaneous equation model with dynamic panel data.  Keywords:2 SLS GMM-AB, Arellano and Bond estimator, Dynamic Panel Data, Simultaneous Equations

scholarly journals Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

2021 ◽  
Vol 6 (3) ◽  
pp. 26
Author(s):  
Christoph Brandstetter ◽  
Sina Stapelfeldt
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Structural Vibration ◽  
Experimental Investigations ◽  
Vibration Modes ◽  
Critical Problem ◽  
Safety Critical ◽  
Unstable Vibration ◽  
Aero Engines ◽  
Lock In

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

Examination of customer-centric measures among different types of customers in the context of major Canadian ski resort

2018 ◽  
Vol 30 (2) ◽  
pp. 438-459
Author(s):  
Matti J. Haverila ◽  
Kai Christian Haverila
Keyword(s):  
Customer Satisfaction ◽  
Structural Equation ◽  
A Priori ◽  
Equation Modeling ◽  
Marketing Practice ◽  
Content Type ◽  
Ski Resort ◽  
Different Types ◽  
Managerial Implications ◽  
Satisfaction Model

Purpose Customer-centric measures such as customer satisfaction and repurchase intent are important indicators of performance. The purpose of this paper is to examine what is the strength and significance of the path coefficients in a customer satisfaction model consisting of various customer-centric measures for different types of ski resort customer (i.e. day, weekend and ski holiday visitors as well as season pass holders) in a ski resort in Canada. Design/methodology/approach The results were analyzed using the partial least squares structural equation modeling approach for the four different types ski resort visitors. Findings There appeared to differences in the strength and significance in the customer satisfaction model relationships for the four types of ski resort visitors indicating that the a priori managerial classification of the ski resort visitors is warranted. Originality/value The research pinpoints differences in the strength and significance in the relationships between customer-centric measures for four different types ski resort visitors, i.e. day, weekend and ski holiday visitors as well as season pass holders, which have significant managerial implications for the marketing practice of the ski resort.

Estimation of a Structural Equation when Reduced Form Coefficients are Known

1986 ◽  
Vol 2 (3) ◽  
pp. 445-446
Author(s):  
Cheng Hsiao ◽  
Kimio Morimune
Keyword(s):  
Structural Equation ◽  
Reduced Form

scholarly journals A Cascaded Unsupervised Model for PoS Tagging

2021 ◽  
Vol 20 (1) ◽  
pp. 1-23
Author(s):  
Necva Bölücü ◽  
Burcu Can
Keyword(s):  
Linear Model ◽  
Language Processing ◽  
Bayesian Model ◽  
Linear Models ◽  
Syntactic Category ◽  
Semantic Parsing ◽  
Pos Tagging ◽  
Part Of Speech ◽  
Sentence Level ◽  
Log Linear

Part of speech (PoS) tagging is one of the fundamental syntactic tasks in Natural Language Processing, as it assigns a syntactic category to each word within a given sentence or context (such as noun, verb, adjective, etc.). Those syntactic categories could be used to further analyze the sentence-level syntax (e.g., dependency parsing) and thereby extract the meaning of the sentence (e.g., semantic parsing). Various methods have been proposed for learning PoS tags in an unsupervised setting without using any annotated corpora. One of the widely used methods for the tagging problem is log-linear models. Initialization of the parameters in a log-linear model is very crucial for the inference. Different initialization techniques have been used so far. In this work, we present a log-linear model for PoS tagging that uses another fully unsupervised Bayesian model to initialize the parameters of the model in a cascaded framework. Therefore, we transfer some knowledge between two different unsupervised models to leverage the PoS tagging results, where a log-linear model benefits from a Bayesian model’s expertise. We present results for Turkish as a morphologically rich language and for English as a comparably morphologically poor language in a fully unsupervised framework. The results show that our framework outperforms other unsupervised models proposed for PoS tagging.

Application of non-linear turbulence models in an engine-type flow configuration

2007 ◽  
Vol 8 (5) ◽  
pp. 449-464 ◽  
Author(s):  
C. H. Son ◽  
T. A. Shethaji ◽  
C. J. Rutland ◽  
H Barths ◽  
A Lippert ◽  
...  
Keyword(s):  
Experimental Data ◽  
Renormalization Group ◽  
Linear Models ◽  
Combustion Engine ◽  
Mean Flow ◽  
Modest Improvement ◽  
Non Linear ◽  
Standard Linear ◽  
Simple Flows ◽  
Engine Type

Three non-linear k-ε models were implemented into the multi-dimensional computational fluid dynamics code GMTEC with the purpose of comparing them with existing linear k-ε models including renormalization group variations. The primary focus of the present study is to evaluate the potential of these non-linear models in engineering applications such as the internal combustion engine. The square duct flow and the backwards-facing step flow were two simple test cases chosen for which experimental data are available for comparison. Successful simulations for these cases were followed by simulations of an engine-type intake flow to evaluate the performance of the non-linear models in comparison with experimental data and the standard linear k-ε models as well as two renormalization group types. All the non-linear models are found to be an improvement over the standard linear model, but mostly in simple flows. For more complex flows, such as the engine-type case, only the cubic non-linear models appear to make a modest improvement in the mean flow but without any improvement in the root-mean-square values. These improvements are overshadowed by the stiffness of the cubic models and the requirements for smaller time steps. The contributions of each non-linear term to the Reynolds stress tensor are analysed in detail in order to identify the different characteristics of the different non-linear models for engine intake flows.

scholarly journals Linear power-flow analysis method for AC-DC electric power networks

2021 ◽  
Author(s):  
Mohammadreza Vatani
Keyword(s):  
Power Systems ◽  
Linear Model ◽  
Power Flow ◽  
Linear Models ◽  
Power Converters ◽  
Power Balance ◽  
Balance Equations ◽  
Dc Power ◽  
Phase Angles ◽  
Dc Power Systems

AC-DC power systems have been operating more than sixty years. Nonlinear bus-wise power balance equations provide accurate model of AC-DC power systems. However, optimization tools for planning and operation require linear version, even if approximate, for creating tractable algorithms, considering modern elements such as DERs (distributed energy resources). Hitherto, linear models of only AC power systems are available, which coincidentally are called DC power flow. To address this drawback, linear bus-wise power balance equations are developed for AC-DC power systems and presented. As a first contribution, while AC and DC lines are represented by susceptance and conductance elements, AC-DC power converters are represented by a proposed linear relationship. As a second contribution, a three-step linear AC-DC power flow method is proposed. The first step solves the whole network considering it as a linear AC network, yielding bus phase angles at all busses. The second step computes attributes of the proposed linear model of all AC-DC power converters. The third step solves the linear model of the AC-DC system including converters, yielding bus phase angles at AC busses and voltage magnitudes at DC busses. The benefit of the proposed linear power flow model of AC-DC power system, while an approximation of the nonlinear model, enables representation of bus-wise power balance of AC-DC systems in complex planning and operational optimization formulations and hence holds the promise of phenomenal progress. The proposed linear AC-DC power systems is tested on numerous IEEE test systems and demonstrated to be fast, reliable, and consistent.

Sign in / Sign up

Export Citation Format

Share Document