Korelasi Kanonik

Summary

This video explains the concept of canonical correlation, which was discovered by Hotelling. It describes how canonical correlation assesses the relationship between a predictor group (independent variables) and a response group (dependent variables). The process involves finding linear combinations of predictor and response variables with the goal of maximizing correlation. The video also discusses the assumptions needed for the analysis, such as normality and the absence of multicollinearity, and provides a step-by-step guide on how to conduct canonical correlation using SPSS. The tutorial is complemented with an example to help clarify the method.

Takeaways

• 😀 Canonical correlation is a statistical method that measures the relationship between two sets of variables: the predictor group (independent variables) and the response group (dependent variables).
• 😀 The method was developed by Harold Hotelling and seeks to find linear combinations of the predictor and response variables that are maximally correlated.
• 😀 The test requirements for using canonical correlation include normality (tested by the Kolmogorov-Smirnov test) and the absence of multicollinearity (correlation coefficient greater than 0.8 indicates multicollinearity).
• 😀 Canonical correlation analysis can be performed using either a correlation matrix (standardized data) or a covariance matrix (actual data).
• 😀 The canonical weight, load, and cross-load are key metrics used to interpret the results: the weight shows the contribution of original variables, the load measures relationships with canonical variables, and the cross-load indicates relationships with non-canonical variables.
• 😀 Redundancy, calculated as R-square (square of the canonical correlation), is used to determine the proportion of variance explained by the canonical variables.
• 😀 There are two types of hypothesis tests in canonical correlation analysis: the joint hypothesis test (testing the significance of all canonical functions) and the individual hypothesis test (testing each canonical function).
• 😀 A typical example involves studying the relationship between banking disintermediation (measured by variables like LDR and NPL) and economic indicators like national income (GDP) and domestic investment (IDM).
• 😀 SPSS can be used to perform canonical correlation analysis by inputting data and running specific syntax that generates results for the canonical functions and their significance.
• 😀 The results show the canonical correlation values, the significance of the functions, and the interpretation of canonical coefficients. The first canonical function often explains the largest proportion of variance in the dependent variables.

Q & A

What is canonical correlation?

Canonical correlation is the relationship between a set of independent variables (predictors) and a set of dependent variables (responses). It aims to find linear combinations of both groups that maximize the correlation between them.

Who developed canonical correlation analysis?

Canonical correlation was developed by Harold Hotelling.

What are the key requirements for performing canonical correlation analysis?

The two key requirements are normality and the absence of multicollinearity. Normality is tested using the Kolmogorov-Smirnov test, and multicollinearity is checked by ensuring that the correlation between variables does not exceed 0.8.

How is normality tested in canonical correlation analysis?

Normality is tested using the Kolmogorov-Smirnov test. If the p-value is smaller than the significance level (alpha), the data is considered to be normally distributed.

What happens if there is multicollinearity in the data?

If multicollinearity exists, meaning the correlation coefficient between independent variables or dependent variables exceeds 0.8, it indicates that the results may not be reliable. In such cases, data transformation or variable elimination is recommended.

What are the two methods used to compute canonical functions?

Canonical functions can be computed using either the correlation matrix or the covariance matrix. The correlation matrix standardizes the data, while the covariance matrix uses actual data values.

What is the purpose of canonical weights in canonical correlation analysis?

Canonical weights indicate the contribution of the original variables to the canonical variables. They help in understanding how each original variable contributes to the formation of the canonical variables.

What does redundancy mean in the context of canonical correlation analysis?

Redundancy refers to the proportion of variance that can be explained by the canonical variable. It is calculated using R-squared (the square of the canonical correlation).

What is the difference between a joint hypothesis test and an individual hypothesis test in canonical correlation analysis?

The joint hypothesis test assesses whether there is a significant relationship between the two sets of variables as a whole. The individual hypothesis test evaluates the significance of each canonical correlation function separately.

How do you interpret the p-values in the significance tests for canonical functions?

If the p-value is smaller than the significance level (alpha, typically 0.05), you reject the null hypothesis, indicating that the canonical function is significant. If the p-value is larger, you accept the null hypothesis, suggesting the canonical function is not significant.