Health vs. Attitudinal Analysis
Unsupervised Learning: Canonical Correlation Analysis
Canonical Correlation Analysis (CCA) is a Multivariate Statistics technique that allows you to analyze correlations between two datasets. Canonical Correlation Analysis can be used to model the correlations between two datasets in two ways:
Focusing on a dependence relationship, and model the two datasets in a regression-like manner: data set y as a function of data set x.
Focusing on the exploration of the relationships between the two datasets without stating any data set as the dependent or the independent variables. You could compare it with methods like PCA or Factor Analysis in this case.
For this analysis, we use CCA to show linear correlations between the two sets of variables--health dataset and attitudinal dataset.
Using Wilks’ Lambda for CCA 1, we get an f-test of 0.7999, approx. of 5.2003, a df1 of 20, df2 of 1493.43, and p-value of 7.8537e-13. We reject the null hypothesis since the CCA 1 does not equal zero because the p- value is below 0.05
Using Wilks’ Lambda for CCA2, we get an f-test of 0.9323, approx. of 2.67219, a df1 of 12, a df2 of 1193.53, and a p-value: 1.4986e-03. We reject the null hypothesis since the CCA 2 does not equal zero because the p-value is below 0.05
As seen for above the first strongest CCA 1between Health, X, and Attitudinal, Y is a mere 0.3768. While from the second CCA 2 is a low of 0.2471.
And as can be seen in the plots in the appendix the scatterplot of the Y and X scores do not show a strong relationship for both CCA 1 and CCA 2
For Health, the variables that contribute the most is mental health with the score of 0.98 and coefficient of 0.0123. It has a mediocre correlation, 0.506, to physical health.
As for Attitudinal, the variable that contribute the most is control with the score of 0.78 and coefficient of 0.022. It has a weak correlation, 0.347, with self-esteem.
In conclusion, there is a weak CC between Health and Attitudinal.
For CCA 1:
Health,
X = 0.0123*menheal-0.0016*phyheal-0.0004*timedrs+0.0019*attdrug-0.0006*druguse
Attitudinal,
Y =0.022*control+0.0028*attmar+0.0028*esteem-0.0009*attrole
For CCA 2:
Health,
X = -0.001*menheal+0.0048*phyheal+0.0009*timedrs-0.035*attdrug+0.0039*druguse
Attitudinal,
Y = -0.0003*control+0.0024*attmar-0.0079*esteem+0.004*attrole
Appendix
