A panel model for political efficacy and responsiveness: an application of LISREL 7 with weighted least squares

Political efficacy is considered to be one of the most important attitudes in theories of political participation and democratic politics. It has been assumed that political efficacy is a stable, persistent orientation rather than a transient attitude. Several studies have examined the stability of political efficacy over time. In most of these studies, based on the analysis of the traditional SRC items, the stability assumption has been questioned. In this paper, we reconsider the stability issue but we adopt a different approach. We distinguish between two components of political efficacy: internal efficacy, a personal attribute and responsiveness, a system attribute, and we study their stability over time. To study the stability of political efficacy and responsiveness over time, we analyse the data with PRELIS and we develop a panel model using LISREL 7. As the observed variables are only ordinal, the estimation of the parameters of the model is based on polychoric correlations and on the weighted least squares method. Our analysis makes use of the Political Action Survey panel data for the USA. This data contains the six SRC efficacy items measured at two occasions. We find that the stability coefficients are higher than those reported in previous research. The difference in the values of the stability coefficients for each component seems to indicate that the personal component is more stable than the system component.     

Factor analysis of the Big Five Questionnaire using polychoric correlations in children

Although the Big Five Questionnaire for children (BFQ-C) (C. Barbaranelli et al., Manuale del BFQ-C. Big Five Questionnaire Children, O.S. Organizazioni, Firenze, 1998) is an ordinal scale, its dimensionality has often been studied using factor analysis with Pearson correlations. In contrast, the present study takes this ordinal metric into account and examines the dimensionality of the scale using factor analysis based on a matrix of polychoric correlations. The sample comprised 852 subjects (40.90% boys and 59.10% girls). As in previous studies the results obtained through exploratory factor analysis revealed a five-factor structure (extraversion, agreeableness, conscientiousness, emotional instability and openness). However, the results of the confirmatory factor analysis were consistent with both a four and five-factor structure, the former showing a slightly better fit and adequate theoretical interpretation. These data confirm the need for further research as to whether the factor ‘Openness’ should be maintained as an independent factor (five-factor model), or whether it would be best to omit it and distribute its items among the factors ‘Extraversion’ and ‘Conscientiousness’ (four-factor model).     

Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables

Given that the use of Likert scales is increasingly common in the field of social research it is necessary to determine which methodology is the most suitable for analysing the data obtained; although, given the categorization of these scales, the results should be treated as ordinal data it is often the case that they are analysed using techniques designed for cardinal measures. One of the most widely used techniques for studying the construct validity of data is factor analysis, whether exploratory or confirmatory, and this method uses correlation matrices (generally Pearson) to obtain factor solutions. In this context, and by means of simulation studies, we aim to illustrate the advantages of using polychoric rather than Pearson correlations, taking into account that the latter require quantitative variables measured in intervals, and that the relationship between these variables has to be monotonic. The results show that the solutions obtained using polychoric correlations provide a more accurate reproduction of the measurement model used to generate the data.     

Out-of-sample forecasts of China's economic growth and inflation using rolling weighted least squares

Macroeconomic forecasting in China is essential for the government to take proper policy decisions on government expenditure and money supply, among other matters. The existing literature on forecasting Chinas macroeconomic variables is unclear on the crucial issue of how to choose an optimal window to estimate parameters with rolling out-of-sample forecasts. This study fills this gap in forecasting economic growth and inflation in China, by using the rolling weighted least squares (WLS) with the practically feasible cross-validation (CV) procedure of Hong et al. (2018) to choose an optimal estimation window. We undertake an empirical analysis of monthly data on up to 30 candidate indicators (mainly asset prices) for a span of 17 years (2000–2017). It is documented that the forecasting performance of rolling estimation is sensitive to the selection of rolling windows. The empirical analysis shows that the rolling WLS with the CV-based rolling window outperforms other rolling methods on univariate regressions in most cases. One possible explanation for this is that these macroeconomic variables often suffer from structural changes due to changes in institutional reforms, policies, crises, and other factors. Furthermore, we find that, in most cases, asset prices are key variables for forecasting macroeconomic variables, especially output growth rate.     

MSE-improvement of the least squares estimator by dropping variables

It is well known that dropping variables in regression analysis decreases the variance of the least squares (LS) estimator of the remaining parameters. However, after elimination estimates of these parameters are biased, if the full model is correct. In his recent paper, Boscher (1991) showed that the LS-estimator in the special case of a mean shift model (cf. Cook and Weisberg, 1982) which assumes no “outliers” can be considered in the framework of a linear regression model where some variables are deleted. He derived conditions under which this estimator outperforms the LS-estimator of the full model in terms of the mean squared error (MSE)-matrix criterion. We demonstrate that this approach can be extended to the general set-up of dropping variables. Necessary and sufficient conditions for the MSE-matrix superiority of the LS-estimator in the reduced model over that in the full model are derived. We also provide a uniformly most powerful F-statistic for testing the MSE-improvement.     

On consistency of the weighted least squares estimators in a semiparametric regression model

This paper is concerned with the semiparametric regression model \(y_i=x_i\beta +g(t_i)+\sigma _ie_i,~~i=1,2,\ldots ,n,\) where \(\sigma _i^2=f(u_i)\), \((x_i,t_i,u_i)\) are known fixed design points, \(\beta \) is an unknown parameter to be estimated, \(g(\cdot )\) and \(f(\cdot )\) are unknown functions, random errors \(e_i\) are widely orthant dependent random variables. The p-th (\(p>0\)) mean consistency and strong consistency for least squares estimators and weighted least squares estimators of \(\beta \) and g under some more mild conditions are investigated. A simulation study is also undertaken to assess the finite sample performance of the results that we established. The results obtained in the paper generalize and improve some corresponding ones of negatively associated random variables.     

Corrections for coarsely categorized measures: LISREL's polyserial and polychoric correlations

Versions 5 and 6 of LISREL (Joreskog and Sorbom, 1981) contain procedures that estimate the underlying correlation between continuous variables on the basis of crude rank category measures. The procedures assume that the distribution of the measured variables would have been bivariate normal if they had not been categorized. Using survey data and simulations, the accuracy of these polyserial/polychoric (P/P) based estimates of the underlying correlations are compared with those based on simple equal distance scoring of the categories. The results indicate that under some conditions, e.g., nearly normally distributed variables and moderate to high correlations, the polyserial/polychoric based estimates are better. Under other conditions, e.g., a moderate to high degree of skew and kurtosis and low correlations, the equal distance score based estimates are better. Under all conditions, the amount of error decreases fairly rapidly as the number of categories is increased from two to five.     

Improved forecasting of autoregressive series by weighted least squares approximate REML estimation

Restricted maximum likelihood (REML) estimation has recently been shown to provide less biased estimates in autoregressive series. A simple weighted least squares approximate REML procedure has been developed that is particularly useful for vector autoregressive processes. Here, we compare the forecasts of such processes using both the standard ordinary least squares (OLS) estimates and the new approximate REML estimates. Forecasts based on the approximate REML estimates are found to provide a significant improvement over those obtained using the standard OLS estimates.     

Nonparametric regression function estimation using interaction least squares splines and comlexity regularization

Let (X, Y) be a pair of random variables withsupp(X)⊆[0,1] ^l andEY ²<∞. Letm ^* be the best approximation of the regression function of (X, Y) by sums of functions of at mostd variables (1≤d≤l). Estimation ofm ^* from i.i.d. data is considered. For the estimation interaction least squares splines, which are defined as sums of polynomial tensor product splines of at mostd variables, are used. The knot sequences of the tensor product splines are chosen equidistant. Complexity regularization is used to choose the number of the knots and the degree of the splines automatically using only the given data. Without any additional condition on the distribution of (X, Y) the weak and strongL ₂-consistency of the estimate is shown. Furthermore, for everyp≥1 and every distribution of (X, Y) withsupp(X)⊆[0,1] ^l ,y bounded andm ^* p-smooth, the integrated squared error of the estimate achieves up to a logarithmic factor the (optimal) rate      

Nonparametric state price density estimation using constrained least squares and the bootstrap

The economic theory of option pricing imposes constraints on the structure of call functions and state price densities. Except in a few polar cases, it does not prescribe functional forms. This paper proposes a nonparametric estimator of option pricing models which incorporates various restrictions (such as monotonicity and convexity) within a single least squares procedure. The bootstrap is used to produce confidence intervals for the call function and its first two derivatives and to calibrate a residual regression test of shape constraints. We apply the techniques to option pricing data on the DAX.     

Estimation and inference in unstable nonlinear least squares models

There is compelling evidence that many macroeconomic and financial variables are not generated by linear models. This evidence is based on testing linearity against either smooth nonlinearity or piece-wise linearity, but there is no framework that encompasses both. This paper provides an econometric framework that allows for both breaks and smooth nonlinearity in between breaks. We estimate the unknown break-dates simultaneously with other parameters via nonlinear least-squares. Using new central limit results for nonlinear processes, we provide inference methods on break-dates and parameter estimates and several instability tests. We illustrate our methods via simulated and empirical smooth transition models with breaks.     

A general analysis of bias in the estimated standard errors of least squares coefficients

It is well known that when errors in the usual regression model are not independently distributed with equal variances, the application of ordinary least squares leads to calculated variances of the coefficient estimates which are biased and inconsistent. The nature of this bias has been investigated extensively, but the existing literature is limited in two significant ways. First, derivations of exact expressions for the bias have been restricted to special cases and, except for the simplest of these, the expressions derived are almost unmanageably complex. Second, for general error specifications, attention has been focused exclusively on deriving bounds for the bias, which are usually wide and do not allow even the probable direction of any bias to be determined. This paper derives an asymptotic expression for the bias which allows both its sign and approximate magnitude to be described easily in most regression problems. This expression is then used to investigate the bias in the cases of serial correlation of an arbitrary degree, variance components models and approximation of a non-linear relationship with a linear specification.     

Selection of influential variables in ordinal data with preponderance of zeros

Presence of excess zero in ordinal data is pervasive in areas like medical and social sciences. Unfortunately, analysis of such kind of data has so far hardly been looked into, perhaps for the reason that the underlying model that fits such data, is not a generalized linear model. Obviously some methodological developments and intensive computations are required. The current investigation is concerned with the selection of variables in such models. In many occasions where the number of predictors is quite large and some of them are not useful, the maximum likelihood approach is not the automatic choice. As, apart from the messy calculations involved, this approach fails to provide efficient estimates of the underlying parameters. The proposed penalized approach includes ?₁ penalty (LASSO) and the mixture of ?₁ and ?₂ penalties (elastic net). We propose a coordinate descent algorithm to fit a wide class of ordinal regression models and select useful variables appearing in both the ordinal regression and the logistic regression based mixing component. A rigorous discussion on the selection of predictors has been made through a simulation study. The proposed method is illustrated by analyzing the severity of driver injury from Michigan upper peninsula road accidents.     

On the efficiency of least squares estimators in non-linear models

Summary  The identity of least squares estimators å and maximum likelihood estimators â is studied in non-linear models of the type z = g ( a ), where z are observable quantities with a probability density function pr ( z ). This identity was proved for independent random variables z and for distributions pr ( z ), of which the arithmetic sample mean is an optimal estimate.     

Mean estimation bias in least squares estimation of autoregressive processes

Estimation of the parameters of an autoregressive process with a mean that is a function of time is considered. Approximate expressions for the bias of the least squares estimator of the autoregressive parameters that is due to estimating the unknown mean function are derived. For the case of a mean function that is a polynomial in time, a reparameterization that isolates the bias is given. Using the approximate expressions, a method of modifying the least squares estimator is proposed. A Monte Carlo study of the second-order autoregressive process is presented. The Monte Carlo results agree well with the approximate theory and, generally speaking, the modified least squares estimators performed better than the least squares estimator. For the second-order process we also considered the empirical properties of the estimated generalized least squares estimator of the mean function and the error made in predicting the process one, two and three periods in the future.     

On the efficiency of least squares estimators in non-linear models

Summary The identity of least squares estimators å and maximum likelihood estimators â is studied in non-linear models of the type z=g(a), where z are observable quantities with a probability density function pr(z). This identity was proved for independent random variables z and for distributions pr(z), of which the arithmetic sample mean is an optimal estimate.     

Consistency and asymptotic normality of least squares estimators in generalized STAR models

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkova et al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.