Exam 1

1. Metainformation

   Tag	Value
   file	Assumptions_uu-communalities-006-en_uu-communalities-006-en
   name	uu-Communalities-006-en
   section	Factor analysis/Communalities
   type	schoice
   solution	TRUE, FALSE, FALSE, FALSE
   Type	Interpreting output
   Language	English
   Level	Statistical Literacy

   Question

   A study of internalising and externalising problem behaviours (X1 to X5) in rural youth resulted in the following correlation matrix:

   

   The communality h2 of variable X5 (PSYCHOSOMATIC) is equal to .61.

   Of which of the problem behaviours listed below is the explained variance of the two-factor solution higher?

   
   
   1. TRUE: X1 crime
   2. FALSE: X2 vandalism
   3. FALSE: X3 depression
   4. FALSE: X4 eating disorders
   
   

   Solution

   Explanation: To calculate the explained variance of each variable, the communality for each variable needs to be calculated. To do this, the following formula is used:

   $h^2_g = sum a^2_{gt} ,$ This formula indicates that the communality of a variable is the sum of its quantised factor loadings. Below, this is done for the four variables:

   $h^2_{x1criminality} = .67^2 + .53^2 = .449+ .281 =.73$ $h^2_{x2vandalism} = .63^2 + .17^2 = .397 + .004 = .40$ $h^2_{x3depression} = .76^2 + -.13^2 = .578 + .017 =.60$ $h^2_{x4eatingdisorders} = .67^2 + -.21^2 = .449 + .044 = .49$