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Related Concept Videos

Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
Friedman Two-way Analysis of Variance by Ranks01:21

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures from...
Coefficient of Correlation01:12

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
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Microsoft Excel: Pearson's Correlation01:18

Microsoft Excel: Pearson's Correlation

Microsoft Excel is a powerful tool for statistical analysis, including calculating Pearson's correlation coefficient, which measures the strength and direction of a linear relationship between two continuous variables. Pearson's correlation coefficient, often denoted as "r," ranges from -1 to 1. A value close to 1 indicates a strong positive correlation, meaning as one variable increases, the other does too. A value close to -1 indicates a strong negative correlation, implying that as one...
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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Ridge structural equation modelling with correlation matrices for ordinal and continuous data.

Ke-Hai Yuan1, Ruilin Wu, Peter M Bentler

  • 1University of Notre Dame, Indiana 46556, USA. kyuan@nd.edu

The British Journal of Mathematical and Statistical Psychology
|April 22, 2011
PubMed
Summary

This study introduces a ridge procedure for structural equation modeling (SEM) using ordinal and continuous data. The new method improves convergence, reduces bias, and enhances model evaluation compared to maximum likelihood procedures.

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Area of Science:

  • Statistics
  • Quantitative Psychology
  • Econometrics

Background:

  • Structural Equation Modeling (SEM) is a versatile statistical technique used for analyzing complex relationships between variables.
  • Traditional SEM methods often face challenges with mixed data types (ordinal and continuous) and convergence issues.
  • Existing procedures may exhibit bias and larger errors, particularly with ordinal data.

Purpose of the Study:

  • To develop and evaluate a novel ridge procedure for SEM that accommodates both ordinal and continuous data.
  • To improve the statistical properties of parameter estimates and overall model fit.
  • To offer a more robust alternative to existing SEM methodologies.

Main Methods:

  • The proposed ridge procedure models the polychoric/polyserial/product-moment correlation matrix R.
  • It fits a structural model to R(a) = R + aI by minimizing a normal distribution-based discrepancy function (where a > 0).
  • Statistical properties of parameter estimates were derived, and four model evaluation statistics were proposed.

Main Results:

  • The ridge procedure demonstrated a better convergence rate for SEM with ordinal data.
  • Empirical results showed smaller bias and mean square error compared to the maximum likelihood procedure.
  • The proposed method yielded better overall model evaluation statistics.

Conclusions:

  • The ridge procedure offers a statistically sound and empirically superior approach for SEM with mixed data types.
  • It addresses limitations of traditional methods, particularly for ordinal data analysis.
  • This technique enhances the reliability and accuracy of SEM analyses in various quantitative fields.