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.     

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.     

Consistent estimation of correlations between observed interval variables with skewed distributions

Departures from multinormality due to skewness in observed distributions may result in inconsistent estimates of product-moment correlations between interval variables. Therefore, the robustness of the product-moment correlation estimator against skewness in the distributions of sample data on interval variables has been investigated. This estimator is robust against skewness of maximally about 1 in absolute value. If the observed distributions have larger skewnesses, the sample data on interval variables may be redistributed over normally distributed discrete variables with 10 categories each. The estimated polychoric correlations between these discrete variables represent consistent estimates of the product-moment correlations between the original interval variables in the population.     

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).     

The Ordinal Controversy Revisited

We present a discussion of the different dimensions of the ongoing controversy about the analysis of ordinal variables. The source of this controversy is traced to the earliest possible stage, measurement theory. Three major approaches in analyzing ordinal variables, called the non-parametric, the parametric, and the underlying variable approach, are identified and the merits and drawbacks of each of these approaches are pointed out. We show that the controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association, and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models. We conclude that the discussion with regard to ordinal variable modeling can only be fruitful if one makes a distinction between different types of ordinal variables. Five types of ordinal variables were identified. The problems concerning the analysis of these five types of ordinal variables are solved in some cases and remain a problem for others.     

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.     

How important is family background for labor-economic outcomes?

This paper uses Swedish register data to examine four classical outcomes in empirical labor economics: IQ, noncognitive skills, years of schooling and long-run earnings. We estimate sibling correlations – and the variance components that define the sibling correlation – in these outcomes. We also estimate correlations for MZ-twins, who share all genes. We also extend the variance-component decomposition by accounting for birth order. We find that conventional intergenerational approaches severely underestimate the role of family background, and that future research should follow a more multidimensional approach to the study of family background.     

Measuring correlations of integrated but not cointegrated variables: A semiparametric approach

Many macroeconomic and financial variables are integrated of order one (or I(1)) processes and are correlated with each other but not necessarily cointegrated. In this paper, we propose to use a semiparametric varying coefficient approach to model/capture such correlations. We propose two consistent estimators to study the dependence relationship among some integrated but not cointegrated time series variables. Simulations are used to examine the finite sample performances of the proposed estimators.     

Interpretation problems of the partial correlation with nonnormally distributed variables

The partial correlation is a commonly used measure for assessing the bivariate correlation of two quantitative variables after eliminating the influence of one or more other variables. The partial correlation is generally interpreted as the correlation that would result if the variables to be eliminated were fixed (not allowed to vary and influence the other variables), which is referred to in the statistical literature as conditional correlation. The present paper demonstrates, by means of theoretical derivations and practical examples, that when the assumption of multivariate normality is violated (e.g., as a result of nonlinear relationships among the variables investigated) the usual interpretation of the partial correlation coefficient will be basically incorrect. In extreme cases the value of the partial correlation coefficient may be strongly positive, close to 1, whereas the conditional correlation may have a large negative value. To solve this problem the paper suggests to partial out a certain function (in most cases the square) of the variables whose effects are to be eliminated if nonlinear relationships are likely to occur.     

Scaling criterion of questionnaire items

Criterion scaling is a technique for scaling questionnaire item responses so as to maximize their correlation with an external criterion. The correlation between the criterion and the scaled item is equal to the correlation ratio or η coefficient. The results of rescaling the ninth grade questionnaire of the “Equal Educational Opportunity Survey” is presented and compared to the subjective scaling used in the Report. Criterion scaling increased all correlations but the change is not substantial enough to change the interpretation of the Report.     

Evaluating estimation methods for ordinal data in structural equation modeling

This study examined the performance of two alternative estimation approaches in structural equation modeling for ordinal data under different levels of model misspecification, score skewness, sample size, and model size. Both approaches involve analyzing a polychoric correlation matrix as well as adjusting standard error estimates and model chi-squared, but one estimates model parameters with maximum likelihood and the other with robust weighted least-squared. Relative bias in parameter estimates and standard error estimates, Type I error rate, and empirical power of the model test, where appropriate, were evaluated through Monte Carlo simulations. These alternative approaches generally provided unbiased parameter estimates when the model was correctly specified. They also provided unbiased standard error estimates and adequate Type I error control in general unless sample size was small and the measured variables were moderately skewed. Differences between the methods in convergence problems and the evaluation criteria, especially under small sample and skewed variable conditions, were discussed.     

Value-creating functions,satisfaction and loyalty in business markets: a categorical variable approach using a robust methodology under structural equation modeling

This paper studies the effect of the value-creating functions on satisfaction and loyalty in business markets. The conceptual framework that depicts a direct effect of the manufacturer’s value-creating functions on the distributor’s satisfaction and loyalty also considers the existence of quadratic effects between satisfaction and loyalty. We used polychoric correlations (Br J Math Stat Psychol 48:339–358, 1995), together with a robust methodological approach, to analyze categorical variables under structural equation modeling (SEM) in EQS. The empirical results are based on a sample of 181 manufacturing companies located in Spain. By using the aforementioned efficient analytical procedure, the results provide strong empirical support that value creation, understood from a functionalist perspective, is an antecedent of satisfaction and loyalty in business-to-business contexts. Distributor satisfaction is significantly affected by the benefit, volume, and safeguard functions, and the indirect value-creating functions performed by the manufacturer. Distributor loyalty is directly influenced by the indirect value-creating functions, but there is no confirmation that the benefit, volume, and safeguard functions do so. Finally, distributor satisfaction does not exert any significant quadratic effect on distributor loyalty but it has a direct linear effect on that variable.     

Walkability and the built environment: validation of the Neighborhood Environment Walkability Scale (NEWS) for urban areas in Mexico

The article gives the results of adjusting an abbreviated version of the Neighborhood Environment Walkability Scale to the situation in Mexico. The results were obtained through the application of 156 instruments to individuals selected through a probability sampling in the metropolitan area of Monterrey, in the state of Nuevo León, Mexico. The validation process was done over four stages; in the first stage, the questions were analyzed and the sampling was adjusted. In the second stage, a factor analysis was carried out; as the questions were Likert-scale type, we use principal components with a matrix of polychoric correlations. In the third stage, the ordinal and non-ordinal Cronbach Alpha coefficients were determined, as were the ordinal and non-ordinal McDonald Omega coefficients, showing that the non-ordinal ones tend to underestimate the level of reliability, as they assume that it is a continuous scale when in this case it is not; however, the literature shows that these coefficients have been the most used in the validation of this scale. Finally, the intervals of trust were calculated with the bootstrap method, with the goal of incorporating the sensitivity that the coefficients could imply in aspects such as the number of questions, intercorrelations between the questions, and the size of the sample. The results show that the ordinal Alpha and Omega coefficients for the three factors, as well as for the entire scale, will have robust values 95% of the time that the questionnaire is used.     

Information technology and firm performance: the role of supply chain integration

This study analyzes the correlation among integrative information technology (IT), supply chain integration (SCI), and firm performance. The results show that integrative IT is positively associated with firm performance through SCI. However, the results of this study show that integrative IT does not have a positive correlation directly with firm performance. It is considered that in the relationship between integrative IT and firm performance, a new approach such as business process-oriented view arguing that performance is yielded through the primary influence of IT is necessary rather than a traditional view that sets up their direct correlations. The findings have the following implications. First, this study presents an endeavor to investigate the consequences of integrative supply chain strategy. Second, this study provides implications in decision making so that supply chain managers can use IT in an effective way.     

Does financial integration affect real exchange rate volatility and cross-country equity market returns correlation?

Existing empirical studies show that financial integration affects the behavior of average excess returns, cross-country equity market returns (EMR) correlations and real exchange rate (RER) volatility. We employ a recently developed two-country model with recursive preferences, frictionless and complete markets and highly correlated long-run innovations to examine whether full financial integration (i.e. full risk-sharing) affects the US-Canada EMR correlation and the US RER volatility, consistently with existing empirical findings. First, full risk-sharing gives rise to a relatively high RER volatility. Second, it induces very strong positive cross-country EMR correlations. Both quantities are higher than those observed in the US-Canada asset pricing data, and increase as the risk-sharing incentive increases. In contrast, “international consumption quantities” are weakly sensitive to changes in the level of aversion to consumption and utility risk.     

Exchange rate regimes and market integration: evidence from the dynamic relations between renminbi onshore and offshore markets

The Chinese renminbi (RMB) has been on the way of becoming a major international currency. This paper examines the impact of the RMB exchange rate regime and policy on the integration and information flows between RMB onshore and offshore markets. We employ a long sample of daily data encompassing multiple times of RMB exchange rate regime change (peg to managed float in 2005, re-peg in 2008, re-float in 2010, and the central parity reform in 2015), and study the dynamic conditional correlations and spillovers between RMB onshore spot market and offshore non-deliverable forward (NDF) market. It is found that the switch from exchange rate peg to managed float and a widening of the floating band strengthen cross-market correlation and information flows (especially offshore-to-onshore spillovers). A market-learning explanation is offered for the observation that the correlation collapse in the re-peg period was not as prompt as the correlation take-off in the 2005 reform period. These findings have important implications for China’s monetary and foreign exchange policies and shed light on the integration of China’s financial markets with the rest of the world.     

What determines the long-term correlation between oil prices and exchange rates?

In this study, we obtain the long-term correlation between oil prices and exchange rates by employing the dynamic conditional correlation-mixed data sampling (DCC-MIDAS) model. We then identify the factors that influence the long-term correlation using panel data analysis. We find that the long-run correlations between oil prices and exchange rates are negative for all oil-exchange rate markets except Japan. We also find that both inflation and term spread have negative effects, while the risk-free interest rate has a positive effect on the long-term correlation between oil prices and exchange rates. Importantly, the empirical results show that an increase in inflation will significantly damage the real value of the currency itself.     

Monte Carlo evidence on the choice between sample selection and two-part models

This Monte Carlo study examines the relative performance of sample selection and two-part models for data with a cluster at zero. The data are drawn from a bivariate normal distribution with a positive correlation. The alternative estimators are examined in terms of means squared error, mean bias and pointwise bias. The sample selection estimators include LIML and FIML. The two-part estimators include a naive (the true specification, omitting the correlation coefficient) and a data-analytic (testimator) variant.In the absence of exclusion restrictions, the two-part models are no worse, and often appreciably better than selection models in terms of mean behavior, but can behave poorly for extreme values of the independent variable. LIML had the worst performance of all four models. Empirically, selection effects are difficult to distinguish from a non-linear (e.g., quadratic) response. With exclusion restrictions, simple selection models were significantly better behaved than a naive two-part model over subranges of the data, but were negligibly better than the data-analytic version.     

Robustness of statistical inferences using linear models with meta-analytic correlation matrices

To examine complex relationships among variables, researchers in human resource management, industrial-organizational psychology, organizational behavior, and related fields have increasingly used meta-analytic procedures to aggregate effect sizes across primary studies to form meta-analytic correlation matrices, which are then subjected to further analyses using linear models (e.g., multiple linear regression). Because missing effect sizes (i.e., correlation coefficients) and different sample sizes across primary studies can occur when constructing meta-analytic correlation matrices, the present study examined the effects of missingness under realistic conditions and various methods for estimating sample size (e.g., minimum sample size, arithmetic mean, harmonic mean, and geometric mean) on the estimated squared multiple correlation coefficient (R²) and the power of the significance test on the overall R² in linear regression. Simulation results suggest that missing data had a more detrimental effect as the number of primary studies decreased and the number of predictor variables increased. It appears that using second-order sample sizes of at least 10 (i.e., independent effect sizes) can improve both statistical power and estimation of the overall R² considerably. Results also suggest that although the minimum sample size should not be used to estimate sample size, the other sample size estimates appear to perform similarly.     

On the Sources of the Feldstein–Horioka Puzzle across Time and Frequencies

This study quantitatively assesses existing explanations for the Feldstein–Horioka puzzle using time–frequency domain analyses for nine countries for the period 1885–2010. The main findings are summarized as follows. First, large economies (e.g. the United States, Italy) show higher correlations between saving and investment than middle‐sized and small countries do. Second, countries can be grouped into two time‐changing patterns of correlations: inverted U‐shaped and increasing patterns. Third, the fiscal balance seems most related to a positive saving‐investment correlation in many countries. Fourth, a global common factor plays an important role in explaining the Feldstein–Horioka puzzle.