Jodi Elliott wrote: > > From various sources I understand that > it is recommended (required?) that THE PATH FROM THE LATENT VARIABLE TO > ITS CORRESPONDING OBSERVED VARIABLE (LAMBDA) BE FIXED TO A VALUE EQUAL > TO THE SQUARE ROOT OF THE RELIABILITY OF THE OBSERVED SCORE. > > Anyway, my question is this: What is the rationale and/or the justification > for this procedure?

The square root of the reliability coefficient is equal to the correlation between an item and the construct it measures.

Remember that in a test-retest situation, reliability is assessed by correlating each subject's score at time 1 with score at time 2. The path model that would describe this relationship is a single construct that causes score at time 1 and score at time 2. Each causal link from the construct to one of the scores (time 1 or time 2) is represented by a correlation coefficient. The product rule from path analysis allows us to obtain the correlation between time 1 and time 2 (the reliability) by multiplying these two correlation coefficients. Assuming that the scores at both times have equal correlations with the latent construct, then the square root of the reliability is equal to the correlation between an item and the construct.

If you think of reliability in terms of strictly paralell forms (both tests measure the same latent construct with exactly equal means and variances), it's the same path diagram, now labeled form 1 and form 2, rather than time 1 and time 2.

Steven J. Pierce Master's Student in Experimental Psychology Mississippi State University E-Mail: sjp2@ra.msstate.edu WWW: http://www2.msstate.edu/~sjp2/index.html