A framework for power analysis using a structural equation modelling procedure

BACKGROUND: This paper demonstrates how structural equation modelling (SEM) can be used as a tool to aid in carrying out power analyses. For many complex multivariate designs that are increasingly being employed, power analyses can be difficult to carry out, because the software available lacks sufficient flexibility. Satorra and Saris developed a method for estimating the power of the likelihood ratio test for structural equation models. Whilst the Satorra and Saris approach is familiar to researchers who use the structural equation modelling approach, it is less well known amongst other researchers. The SEM approach can be equivalent to other multivariate statistical tests, and therefore the Satorra and Saris approach to power analysis can be used. METHODS: The covariance matrix, along with a vector of means, relating to the alternative hypothesis is generated. This represents the hypothesised population effects. A model (representing the null hypothesis) is then tested in a structural equation model, using the population parameters as input. An analysis based on the chi-square of this model can provide estimates of the sample size required for different levels of power to reject the null hypothesis. CONCLUSIONS: The SEM based power analysis approach may prove useful for researchers designing research in the health and medical spheres

Measuring health inequality among children in developing countries: does the choice of the indicator of economic status matter?

Background Currently, poor-rich inequalities in health in developing countries receive a lot of attention from both researchers and policy makers. Since measuring economic status in developing countries is often problematic, different indicators of wealth are used in different studies. Until now, there is a lack of evidence on the extent to which the use of different measures of economic status affects the observed magnitude of health inequalities. Methods This paper provides this empirical evidence for 10 developing countries, using the Demographic and Health Surveys data-set. We compared the World Bank asset index to three alternative wealth indices, all based on household assets. Under-5 mortality and measles immunisation coverage were the health outcomes studied. Poor-rich inequalities in under-5 mortality and measles immunisation coverage were measured using the Relative Index of Inequality. Results Comparing the World Bank index to the alternative indices, we found that (1) the relative position of households in the national wealth hierarchy varied to an important extent with the asset index used, (2) observed poor-rich inequalities in under-5 mortality and immunisation coverage often changed, in some cases to an important extent, and that (3) the size and direction of this change varied per country, index, and health indicator. Conclusion Researchers and policy makers should be aware that the choice of the measure of economic status influences the observed magnitude of health inequalities, and that differences in health inequalities between countries or time periods, may be an artefact of different wealth measures used

Issues in the construction of wealth indices for the measurement of socio-economic position in low-income countries

BACKGROUND: Epidemiological studies often require measures of socio-economic position (SEP). The application of principal components analysis (PCA) to data on asset-ownership is one popular approach to household SEP measurement. Proponents suggest that the approach provides a rational method for weighting asset data in a single indicator, captures the most important aspect of SEP for health studies, and is based on data that are readily available and/or simple to collect. However, the use of PCA on asset data may not be the best approach to SEP measurement. There remains concern that this approach can obscure the meaning of the final index and is statistically inappropriate for use with discrete data. In addition, the choice of assets to include and the level of agreement between wealth indices and more conventional measures of SEP such as consumption expenditure remain unclear. We discuss these issues, illustrating our examples with data from the Malawi Integrated Household Survey 2004-5. METHODS: Wealth indices were constructed using the assets on which data are collected within Demographic and Health Surveys. Indices were constructed using five weighting methods: PCA, PCA using dichotomised versions of categorical variables, equal weights, weights equal to the inverse of the proportion of households owning the item, and Multiple Correspondence Analysis. Agreement between indices was assessed. Indices were compared with per capita consumption expenditure, and the difference in agreement assessed when different methods were used to adjust consumption expenditure for household size and composition. RESULTS: All indices demonstrated similarly modest agreement with consumption expenditure. The indices constructed using dichotomised data showed strong agreement with each other, as did the indices constructed using categorical data. Agreement was lower between indices using data coded in different ways. The level of agreement between wealth indices and consumption expenditure did not differ when different consumption equivalence scales were applied. CONCLUSION: This study questions the appropriateness of wealth indices as proxies for consumption expenditure. The choice of data included had a greater influence on the wealth index than the method used to weight the data. Despite the limitations of PCA, alternative methods also all had disadvantages

Bayesian Networks for Max-linear Models

We study Bayesian networks based on max-linear structural equations as introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their independence properties. In particular we emphasize that distributions for such networks are generally not faithful to the independence model determined by their associated directed acyclic graph. In addition, we consider some of the basic issues of estimation and discuss generalized maximum likelihood estimation of the coefficients, using the concept of a generalized likelihood ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21]. Finally we argue that the structure of a minimal network asymptotically can be identified completely from observational data.Comment: 18 page

Power calculations using exact data simulation: A useful tool for genetic study designs.

Statistical power calculations constitute an essential first step in the planning of scientific studies. If sufficient summary statistics are available, power calculations are in principle straightforward and computationally light. In designs, which comprise distinct groups (e.g., MZ & DZ twins), sufficient statistics can be calculated within each group, and analyzed in a multi-group model. However, when the number of possible groups is prohibitively large (say, in the hundreds), power calculations on the basis of the summary statistics become impractical. In that case, researchers may resort to Monte Carlo based power studies, which involve the simulation of hundreds or thousands of replicate samples for each specified set of population parameters. Here we present exact data simulation as a third method of power calculation. Exact data simulation involves a transformation of raw data so that the data fit the hypothesized model exactly. As in power calculation with summary statistics, exact data simulation is computationally light, while the number of groups in the analysis has little bearing on the practicality of the method. The method is applied to three genetic designs for illustrative purposes

Validation of a social cohesion theoretical framework: a multiple group SEM strategy

Social cohesion dates back to the end of the nineteenth century. Back then, society experienced epochal transformations, as are also happening nowadays. Whenever there are epochal changes, a social order (cohesion) matter arises. The paper provides a conceptual scheme of social cohesion identifying its constituent dimensions subdivided by three spheres (macro, meso, micro) and two perspectives (objective and subjective). The overarching aim is to test the validity of the operationalization of the social cohesion model provided. Firstly, we conducted an exploratory factor analysis introducing an approach implemented in Mplus named exploratory structural equation modeling that shows several useful characteristics. Afterward, through a structural equation modeling approach, we performed several confirmatory factor analyses adopting a multiple group SEM strategy in order to cross-validate the social cohesion model

The risk of misclassifying subjects within principal component based asset index

The asset index is often used as a measure of socioeconomic status in empirical research as an explanatory variable or to control confounding. Principal component analysis (PCA) is frequently used to create the asset index. We conducted a simulation study to explore how accurately the principal component based asset index reflects the study subjects’ actual poverty level, when the actual poverty level is generated by a simple factor analytic model. In the simulation study using the PC-based asset index, only 1% to 4% of subjects preserved their real position in a quintile scale of assets; between 44% to 82% of subjects were misclassified into the wrong asset quintile. If the PC-based asset index explained less than 30% of the total variance in the component variables, then we consistently observed more than 50% misclassification across quintiles of the index. The frequency of misclassification suggests that the PC-based asset index may not provide a valid measure of poverty level and should be used cautiously as a measure of socioeconomic status

Assessing an organizational culture instrument based on the Competing Values Framework: Exploratory and confirmatory factor analyses

BACKGROUND: The Competing Values Framework (CVF) has been widely used in health services research to assess organizational culture as a predictor of quality improvement implementation, employee and patient satisfaction, and team functioning, among other outcomes. CVF instruments generally are presented as well-validated with reliable aggregated subscales. However, only one study in the health sector has been conducted for the express purpose of validation, and that study population was limited to hospital managers from a single geographic locale. METHODS: We used exploratory and confirmatory factor analyses to examine the underlying structure of data from a CVF instrument. We analyzed cross-sectional data from a work environment survey conducted in the Veterans Health Administration (VHA). The study population comprised all staff in non-supervisory positions. The survey included 14 items adapted from a popular CVF instrument, which measures organizational culture according to four subscales: hierarchical, entrepreneurial, team, and rational. RESULTS: Data from 71,776 non-supervisory employees (approximate response rate 51%) from 168 VHA facilities were used in this analysis. Internal consistency of the subscales was moderate to strong (α = 0.68 to 0.85). However, the entrepreneurial, team, and rational subscales had higher correlations across subscales than within, indicating poor divergent properties. Exploratory factor analysis revealed two factors, comprising the ten items from the entrepreneurial, team, and rational subscales loading on the first factor, and two items from the hierarchical subscale loading on the second factor, along with one item from the rational subscale that cross-loaded on both factors. Results from confirmatory factor analysis suggested that the two-subscale solution provides a more parsimonious fit to the data as compared to the original four-subscale model. CONCLUSION: This study suggests that there may be problems applying conventional CVF subscales to non-supervisors, and underscores the importance of assessing psychometric properties of instruments in each new context and population to which they are applied. It also further highlights the challenges management scholars face in assessing organizational culture in a reliable and comparable way. More research is needed to determine if the emergent two-subscale solution is a valid or meaningful alternative and whether these findings generalize beyond VHA