Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Astivia, Oscar L. Olvera

doi:10.15626/mp.2019.2117

Cited by 11 publications

(5 citation statements)

References 41 publications

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“…Using this method, previous literature has shown the relatively modest impact of underlying nonnormality on SEM estimates based on polychoric correlations (Flora & Curran, 2004; Li, 2016; Rhemtulla et al, 2012). Thus, in line with previous work examining the impact of underlying nonnormality on ordinal data, we used the Vale-Maurelli method to simulate nonnormal data with a univariate skewness of 2 and univariate kurtosis of 7 to represent “moderate” nonnormality (Curran et al, 1996; Olvera Astivia, 2020).…”

Section: Methodsmentioning

confidence: 99%

“…In order for a multivariate distribution to be nonnormal, either the marginal distributions must be nonnormal or the copula of the multivariate distribution must be nonnormal (Foldnes & Olsson, 2016). The copula of data generated using the Vale-Maurelli method is similar to the multivariate normal copula, and thus the data may not be as nonnormally distributed as intended (Olvera Astivia, 2020). Furthermore, work by Grønneberg and Foldnes (2019) and Foldnes and Grønneberg (2020) has demonstrated that discretizing data produced by the Vale-Maurelli method is numerically equivalent to discretizing the intermediate data generated by the multivariate normal distribution, only with different thresholds.…”

Section: Methodsmentioning

confidence: 99%

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Comparing estimation methods for psychometric networks with ordinal data.

Johal¹,

Rhemtulla²

2023

Psychological Methods

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Ordinal data are extremely common in psychological research, with variables often assessed using Likert-type scales that take on only a few values. At the same time, researchers are increasingly fitting network models to ordinal item-level data. Yet very little work has evaluated how network estimation techniques perform when data are ordinal. We use a Monte Carlo simulation to evaluate and compare the performance of three estimation methods applied to either Pearson or polychoric correlations: EBIC graphical lasso with regularized edge estimates ("EBIC"), BIC model selection with partial correlation edge estimates ("BIC"), and multiple regression with p-value-based edge selection and partial correlation edge estimates ("MR"). We vary the number and distribution of thresholds, distribution of the underlying continuous data, sample size, model size, and network density, and we evaluate results in terms of model structure (sensitivity and false positive rate) and edge weight bias.Our results show that the effect of treating the data as ordinal versus continuous depends primarily on the number of levels in the data, and that estimation performance was affected by the sample size, the shape of the underlying distribution, and the symmetry of underlying thresholds. Furthermore, which estimation method is recommended depends on the research goals: MR methods tended to maximize sensitivity of edge detection, BIC approaches minimized false positives, and either one of these produced accurate edge weight estimates in sufficiently large samples. We identify some particularly difficult combinations of conditions for which no method produces stable results.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Comparing estimation methods for psychometric networks with ordinal data.

Johal¹,

Rhemtulla²

2023

Psychological Methods

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“…However, in practice, the normality assumption could also be violated for the variables that underlie the indicators. A plethora of methods exist that could be used to generate underlying nonnormality (e.g., Astivia, 2020;Foldnes & Olsson, 2016). Thus, while LMS-cat and BLMScat have been shown to be robust to the non-normality caused by asymmetrical category thresholds, future research should evaluate their performance with different underlying distributions of the indicators and compare them with other approaches.…”

Section: Limitations and Future Directionsmentioning

confidence: 99%

Latent Variable Interactions with Categorical Indicators: Continuous and Categorical Latent Moderated Structural Equations Approaches

Shen,

Chen,

Somer

et al. 2024

Preprint

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Social science phenomena are often predicted by interactions between variables. When these variables cannot be directly observed, one option is to model them as latent variables that are measured by multiple indicators. When indicators are continuous, latent interactions can be modeled and estimated using the latent moderated structural equations (LMS) approach. A categorical LMS (LMS-cat) approach with full information estimation was more recently developed. While previous research suggests that ordered categorical indicators can sometimes be treated as continuous, LMS and LMS-cat have not yet been directly compared. In this study, we evaluate continuous and categorical LMS for the estimation of latent interactions under ordinal indicators with 2, 3, 5, and 7 categories. Further, we compared the performance of frequentist and Bayesian estimation for both LMS models. Results suggest that categorical approaches are a safer choice, and that frequentist and non-informative Bayesian estimation approaches perform similarly.

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“…These continuous data are then discretized to produce ordinal data. Using this method, previous literature has shown the relatively modest impact of underlying non-normality on SEM estimates based on polychoric correlations (Flora & Curran, 2004;Li, 2016;Rhemtulla et al, 2012 (Curran et al, 1996;Olvera Astivia, 2020).…”

Section: Underlying Distributionmentioning

confidence: 99%

Comparing Estimation Methods for Psychometric Networks with Ordinal Data

Johal¹,

Rhemtulla²

2021

Preprint

View full text Add to dashboard Cite

Ordinal data are extremely common in psychological research, with variables often assessed using Likert-type scales that take on only a few values. At the same time, researchers are increasingly fitting network models to ordinal item-level data. Yet very little work has evaluated how network estimation techniques perform when data are ordinal. We use a Monte Carlo simulation to evaluate and compare the performance of three estimation methods applied to either Pearson or polychoric correlations: EBIC graphical lasso with regularized edge estimates (“EBIC”), BIC model selection with partial correlation edge estimates (“BIC”), and multiple regression with p-value-based edge selection and partial correlation edge estimates (“MR”). We vary the number and distribution of thresholds, distribution of the underlying continuous data, sample size, model size, and network density, and we evaluate results in terms of model structure (sensitivity and false positive rate) and edge weight bias. Our results show that the effect of treating the data as ordinal versus continuous depends primarily on the number of levels in the data, and that estimation performance was affected by the sample size, the shape of the underlying distribution, and the symmetry of underlying thresholds. Furthermore, which estimation method is recommended depends on the research goals: MR methods tended to maximize sensitivity of edge detection, BIC approaches minimized false positives, and either one of these produced accurate edge weight estimates in sufficiently large samples. We identify some particularly difficult combinations of conditions for which no method produces stable results.

show abstract

Issues, problems and potential solutions when simulating continuous, non-normal data in the social sciences

Cited by 11 publications

References 41 publications

Comparing estimation methods for psychometric networks with ordinal data.

Comparing estimation methods for psychometric networks with ordinal data.

Latent Variable Interactions with Categorical Indicators: Continuous and Categorical Latent Moderated Structural Equations Approaches

Comparing Estimation Methods for Psychometric Networks with Ordinal Data

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