🚀 go-pugleaf

In <emu-ct08.cg.1993.0701.095720.nacd@tuda.ncl.ac.uk> Anthony Downing <A.C.Downing@NEWCASTLE.AC.UK> writes:


>1.  Generate a normal distribution of simulated scores on some putative
>    latent trait.
>2.  From this, generate two sets of simulated observable variables, Set A
>    and Set B, such that scores on each of the variables in Set A is
>    jointly determined by
>    i) the answer to the question "Is your latent trait Z-score
>       greater than -0.3, and
>    ii) a bit of randomness, thrown in to stop them all correlating with
>        each other.

>    Variables in Set B are generated similarly, except that the question is
>    "Is your latent trait Z-score greater that +0.3 ?"

>There is no doubt that there is only one latent trait which underlies all
>the variables, but variables within the two sets are similar in their
>degrees of skewness.  Every time I have tried factor analysing such
>simulated data, the result has been at least two factors with eigenvalues
>greater than 1, and at least two factors by the Scree Test - and I have
>never had factor loadings appear with values greater than 1.

But this is precisely what one would expect.   The two sets of
variables are, if I read your method correctly, skewed in opposite
directions, so that within-set correlations will tend to be larger
than between-set correlations.   Hence two (or more) factors.   You
can have even more fun using ternary items of the Yes-Unsure-No
variety, particularly when the instruction is to use the middle
category only infrequently.......

-- 
Steve Blinkhorn <steve@prd.co.uk>