Approximate inference in multivariate nonlinear functional relationships

An estimation procedure based on estimating equations is presented for the parameters in a multivariate functional relationship model, where all observations are subject to error. The covariance matrix of the observational errors may be parametrized and is allowed to be different for different sets of observations. Estimators are defined for the unknown relation parameters and error parameters.
For linear models (i.e. where the model function is linear in the incidental parameters) the estimators are consistent and asymptotically normal. A consistent expression for the covariance matrix of the estimators is derived. The results are valid for general error distributions.
For nonlinear models the estimators are based on locally linear approximations to the model function. The afore mentioned properties of the estimators are now only approximately valid. The adequacy of the approximate inference, based on asymptotic theory for the linearized model, needs at least informal check. Some examples are given to illustrate the estimation procedure.     

An integrated approach to the development of continuous simulations

An integrated approach to the development of Forrester-style simulation models is described. The approach incorporates the concept of an interaction matrix to assist in the development of causal loop diagrams and Dynamo flow diagrams. The interaction matrix is derived from the fundamental notions of system dynamics. Premised upon the presumption that a computer-aided procedure for model formulation can expedite, systematize, and operationalize the model formulation process, the integrated approach utilizes the interaction matrix as a data structure within the computer. An algorithm designed to interface with a remote terminal (such as a CRT display) determines the interaction matrix by interrogating a user until sufficient information about the problem of interest has been obtained. This algorithm is also described in the paper. The interrogations both motivate and facilitate the determination of quantities to be included as well as couplings between the quantities. When a quantity or coupling is designated by a user, the algorithm “knows” its identity at the time of user origination. Both algorithm and matrix are illustrated through recourse to a text-book example and the paper concludes with a summarizing discussion of the possible contribution of such an approach.     

A note on least squares estimation and the blue in a generalized linear regression model

In a generalized linear regression model, least squares and Gauss-Markov estimators differ, in general, if the variance-covariance matrix of the disturbances is singular. In the present note it is shown that, nevertheless, the conventional least squares procedure leads to a Gauss-Markov estimator if it is applied to a modified model which results from adding dummy constraints to the original model. These constraints reflect the effects of the singularity of the variance- convariance matrix. As a consequence, a Gauss-Markov estimate may always be obtained by standard least squares minimization, which offers considerable computational advantages.     

Simultaneous Parameter Estimation in Exploratory Factor Analysis: An Expository Review

The classical exploratory factor analysis (EFA) finds estimates for the factor loadings matrix and the matrix of unique factor variances which give the best fit to the sample correlation matrix with respect to some goodness-of-fit criterion. Common factor scores can be obtained as a function of these estimates and the data. Alternatively to the classical EFA, the EFA model can be fitted directly to the data which yields factor loadings and common factor scores simultaneously. Recently, new algorithms were introduced for the simultaneous least squares estimation of all EFA model unknowns. The new methods are based on the numerical procedure for singular value decomposition of matrices and work equally well when the number of variables exceeds the number of observations. This paper provides an account that is intended as an expository review of methods for simultaneous parameter estimation in EFA. The methods are illustrated on Harman's five socio-economic variables data and a high-dimensional data set from genome research.     

Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions

We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using model selection criteria. We suggest a new two-step model selection procedure which is a hybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency. A Monte Carlo study explores the finite sample performance of this procedure and evaluates the forecasting accuracy of models selected by this procedure. Two empirical applications confirm the usefulness of the model selection procedure proposed here for forecasting.     

A Social Interactions Model with Endogenous Friendship Formation and Selectivity

This paper analyzes the endogeneity bias problem caused by associations of members within a network when the spatial autoregressive (SAR) model is used to study social interactions. When there are unobserved factors that affect both friendship decisions and economic outcomes, the spatial weight matrix (sociomatrix; adjacency matrix) in the SAR model, which represents the structure of a friendship network, might correlate with the disturbance term of the model, and consequently result in an endogenous selection problem in the outcomes. We consider this problem of selection bias with a modeling approach. In this approach, a statistical network model is adopted to explain the endogenous network formation process. By specifying unobserved components in both the network model and the SAR model, we capture the correlation between the processes of network and outcome formation, and propose a proper estimation procedure for the system. We demonstrate that the estimation of this system can be effectively done by using the Bayesian method. We provide a Monte Carlo experiment and an empirical application of this modeling approach on the friendship networks of high school students and their interactions on academic performance in the Add Health data. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymptotically efficient recursive estimation for incomplete data models using the observed information

For a recursive maximum-likelihood estimator with step lengths decaying as 1/n, an adaptive matrix needs to be incorporated to obtain asymptotic efficiency. Ideally, this matrix should be chosen as the inverse Fisher information matrix, which is usually very difficult to compute for incomplete data models. In this paper we give conditions under which the observed information can be incorporated into the recursive procedure to yield an efficient estimator, and we also investigate the finite sample properties of these estimators by simulation.     

矩阵式成本管理在国际工程项目实施中的应用

根据一般矩阵管理模式,以成本管理为例,探讨国际工程项目实施过程中,在公司层面如何进行项目管理的程序、方法及内容,真正做到"管理创效益"。     

Income Distributive Effects in the Brazilian Economy

Studies aiming to evaluate the structural distribution of economic impacts usually treat consumption demand as an exogenous variable. In this case, the Leontief matrix multiplier lacks the multiplier process via the consumption function that one customarily finds in a Keynesian model. To regard the consumption as a fictitious production activity is not the appropriate procedure. Instead, the Keynesian consumption function is introduced at a disaggregated level. For that, a matrix multiplier was formulated in order to combine Leontief's propagation process with the Keynesian propagation process. This matrix includes the effects of endogenous changes in consumption demand. Based on the present production structure in Brazil, the results show how the propagation effect directs the induced income towards capitalists, depriving wage earners. The model also allows for evaluation of diverse effects of the propagation process according to income and consumption coefficients by sector.     

Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags

In this paper we investigate a spatial Durbin error model with finite distributed lags and consider the Bayesian MCMC estimation of the model with a smoothness prior. We study also the corresponding Bayesian model selection procedure for the spatial Durbin error model, the spatial autoregressive model and the matrix exponential spatial specification model. We derive expressions of the marginal likelihood of the three models, which greatly simplify the model selection procedure. Simulation results suggest that the Bayesian estimates of high order spatial distributed lag coefficients are more precise than the maximum likelihood estimates. When the data is generated with a general declining pattern or a unimodal pattern for lag coefficients, the spatial Durbin error model can better capture the pattern than the SAR and the MESS models in most cases. We apply the procedure to study the effect of right to work (RTW) laws on manufacturing employment.     

Markov-switching models with endogenous explanatory variables II: A two-step MLE procedure

This paper proposes a two-step maximum likelihood estimation (MLE) procedure to deal with the problem of endogeneity in Markov-switching regression models. A joint estimation procedure provides us with an asymptotically most efficient estimator, but it is not always feasible, due to the ‘curse of dimensionality’ in the matrix of transition probabilities. A two-step estimation procedure, which ignores potential correlation between the latent state variables, suffers less from the ‘curse of dimensionality’, and it provides a reasonable alternative to the joint estimation procedure. In addition, our Monte Carlo experiments show that the two-step estimation procedure can be more efficient than the joint estimation procedure in finite samples, when there is zero or low correlation between the latent state variables.     

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

Abstract

In this article, we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of a spatial econometric model. An increasing and a decreasing neighbours testing procedure are suggested. Kelejian's J-test for non-nested spatial models is used in the testing procedures. The testing procedures give formal justification for the choice of k, something which has been lacking in the classical spatial econometric literature. Simulations show that the testing procedures can be used in large samples to determine k. An empirical example involving house price data is provided.     

The interchangeability of safety stocks and safety lead time

Due to the uncertainty in estimating both the demand for end products and the supply of components from lower levels, buffering techniques should be included before the loading of a material requirement planning (MRP) system. Safety stocks and safety lead time are two techniques of providing buffering for loading. There have been many studies made concerning the determination of the amount of safety stocks and safety lead time. Some guidelines for choosing between safety stocks and safety lead time for dealing with uncertainty in both demand and supply also have been established. Although these two different methods have been used successfully, it has not been documented that using these two methods in a given situation will yield essentially the same results; that is, the interchangeability of these two buffering techniques has not been explored quantitatively.Since the net influence of safety stocks and safety lead time and their quantitative interchangeability are of major interest, an analytical model is proposed for this study. The lead-time offset procedure for components loading are represented by a matrix model that is based on a lot-for-lot lot-sizing technique. This lead-time offset matrix model is the product of the precedence matrix and the fixed-duration matrix. The precedence matrix is formed according to the total requirement factor matrix and the duration matrix is formed by each component process time. Thus, the lead-time offset matrix will generate the starting period of each component.When the lead-time offset procedure is modeled, the net influence of buffering quantity can be analyzed. The planned safety stock that is normally used to accommodate unexpected demand, shortage in supply, and defects from the operation at each process can be combined with demand to form the master production schedule. The revised lead time due to the integration of the safety stocks can be calculated through the lead-time offset model. The safety lead time may extend the component process time as well as overall production lead time if the designated safety lead time is longer than the available slack time in a fixed lead-time loading system.When the proposed lead-time offset model is further examined, it is found that planned safety stocks at the higher level can buffer the fluctuations of lower level components quantity as well as the fluctuations of same level components quantity. Safety stocks can also buffer shortages that are caused by the delay of raw material and manufacturing processes. Thus, safety stocks can be used to buffer unexpected delay time up to certain limits. A planned safety lead time at higher level component process can buffer the fluctuations of lower level components process time, as well as the same level component process time. The safety lead time can be used to produce additional products to meet unexpected excessive demand up to certain limits under the following conditions: 1. The excessive demand is known before the actual processing of the components in the lowest level. 2. The raw material at the lowest level is available.Although safety stocks and safety lead time are interchangeable in terms of the ability to buffer variations in quantity, the conditions for safety lead time are seldom met in actual practices. Thus, the slack time in a fixed lead-time loading system cannot be considered as an effective measure to substitute safety stocks. However, all or part of the delay in manufacturing processes or the supply from the lower level components can be buffered by the safety stock and the MPS will still be met. From this study, it is obvious that the slack time can be reduced when safety stocks are planned for an MRP system. The reduction of fixed lead-time duration will be beneficial to the overall planning and scheduling in MRP systems.     

Determination of an optimal set of design requirements using house of quality

Quality Function Deployment (QFD) has been used to translate customer needs and wants into technical design requirements in order to increase customer satisfaction. QFD utilizes the house of quality (HOQ), which is a matrix providing a conceptual map for the design process, as a construct for understanding Customer Requirements (CRs) and establishing priorities of Design Requirements (DRs) to satisfy them. Some methodological issues occurring in the conventional HOQ are discussed, and then a new integrative decision model for selecting an optimal set of DRs is presented using a modified HOQ model. The modified HOQ prioritization procedure employs a multi-attribute decision method for assigning relationship ratings between CRs and DRs instead of a conventional relationship rating scale, such as 1–3–9. The proposed decision model has been applied to an indoor air quality improvement problem as an illustrative example.     

Optimal weighted average power similar tests for the covariance structure in the linear regression model

This paper suggests a procedure for the construction of optimal weighted average power similar tests for the error covariance matrix of a Gaussian linear regression model when the alternative model belongs to the exponential family. The paper uses a saddlepoint approximation to construct simple test statistics for a large class of problems and overcomes the computational burden of evaluating the complicated integrals arising in the derivation of optimal weighted average power tests. Extensions to panel data models are considered. Applications are given to tests for error autocorrelation in the linear regression model and in a panel data framework.     

The power of four tests of autocorrelation in the linear regression model

The power of each of four tests of first-order autocorrelation in the linear regression model is determined for a simple and multiple regression model whose parameters are presumed to be known. The tests are: Durbin-Watson bounds test, a test based on Theil's best linear unbiased scalar estimator, a test devised by Abrahamse, Koerts and Louter, and an exact test devised by Durbin.For positive values of the coefficient of autocorrelation the Durbin-Watson bounds test is generally better than the tests based on the estimator proposed by Abrahamse, Koerts and Louter, the best linear unbiased scalar estimator, and the Durbin exact test. For negative values of the coefficient of autocorrelation, the pattern of results is mixed for all four test procedures. A byproduct of these experiments is the demonstrated feasibility of enumerating the distribution of the Durbin-Watson test statistic for any regression matrix and thus eliminating the region of indeterminacy from the Durbin-Watson test procedure.     

Bridging macroeconomic data between statistical classifications: the count-seed RAS approach

ABSTRACT

In applications, it is often necessary to link heavily aggregated macroeconomic datasets adhering to different statistical classifications. We propose a simple data reclassification procedure for those cases in which a bridge matrix grounded in microdata is not available. The essential requirement of our approach, which we refer to as count-seed RAS, is that there exists a time period or a geographical entity similar to the one of interest for which the relevant economic variable is observed according to both classifications. From this information, a bridge matrix is constructed using bi-proportional methods to rescale a seed matrix based on a qualitative correspondence table from official sources. We test the procedure in two case studies and by Monte Carlo methods. We find that, in terms of reclassification accuracy, it performs noticeably better than other expeditious methods. The analytical framework underlying our approach may prove a useful way of conceptualizing data reclassification problems.     

A Note Regarding the Condition Number: The Case of Spurious and Latent Multicollinearity

The detection of multicollinearity in econometric models is usualy based on the so-called condition number (CN) of the data matrix X. However, the computation of the CN, which is the greater condition index, gives misleading results in particular cases and many commercial computer packages produce an inflated CN, even in cases of spurious multicollinearity, i.e. even if no collinearity exists when the explanatory variables are considered. And this is due to the very low total variation of some columns of the transformed data matrix, which is used to compute CN. On the other hand, we may have the problem of latent multocollinearity which can be revealed by additionally computing a revised CN. With all these in mind, we figure out the ill-conditioned situations, suggesting some practical rules of thumb to face such problems using a single diagnostic in a fairly simple procedure. It is noted that this procedure is not mentioned in the relevant literature.     

Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances

Abstract

This paper develops a unified framework for fixed effects (FE) and random effects (RE) estimation of higher-order spatial autoregressive panel data models with spatial autoregressive disturbances and heteroscedasticity of unknown form in the idiosyncratic error component. We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define both an RE and an FE spatial generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators and derive their joint asymptotic distribution, which is robust to heteroscedasticity of unknown form in the idiosyncratic error component. Finally, we derive a robust Hausman test of the spatial random against the spatial FE model.     

A New Method for the Identification of Patterns in Input–Output Matrices

This paper suggests a new algorithm for selecting the input–output (IO) coefficients of a Leontief matrix in order of importance, so providing an analytical method for decomposing an IO matrix. It avoids the choice of arbitrary thresholds for eliminating flows or coefficients, and allows for circular relationships. For this purpose, a simple inverse-important criterion has been chosen, which is consistent with the logic of the Leontief model. A procedure that greatly reduces the computational burden is then devised. This method permits new comparisons of IO structures of different countries or regions, for identifying their different degree of internal integration and their reciprocal influence through the exchange of intermediate goods. An application to an IO model for seven European Community countries for 1980 is then presented.