5 MEASURING THE LATENT VARIABLES
Chapter 6 on methods describes the SEM (Structural Equation Modelling) process
of latent variable modelling in detail. Briefly, however, a latent variable is a
hypothesised variable (also referred as a factor or construct) which is not directly
observable, although its ‘presence’ can be revealed by using confirmatory factor
analysis (CFA) to measure the ‘effects’ of that latent variable on a number of
‘indicator variables’. This is achieved (in simple terms) by measuring the amount
of variance (a measure of dispersal around the mean) shared between the
indicator variables (while also accounting for the degree of unobserved - or error -
variance). Where there is a significantly large level of observed shared variance
(called covariance) between these indicator variables, the latent variable, or
factor, is considered to be ‘manifest’ by its effect on the indicator variables. Put
another way, the existence of substantial shared variance (covariance) between
the observable variables ‘indicates’ the (albeit abstract) existence of the factor.
For example, considering the indicator variables for the Inspirational Motivation
(IM) factor in the Full-Range Leadership Model (FRLM) (Avolio and Bass 2004a:
96). The Multifactor Leadership Questionnaire (MLQ) asks subordinate
respondents to rate their supervisor by responding to each of the following four
statements using a five point scale which is bounded by 0 = Not At All and 4 =
Frequently, If Not Always:
The person I am rating...
Talks optimistically about the future
Talks enthusiastically about what needs to be accomplished
Articulates a compelling vision of the future
Expresses confidence that goals will be achieved
The latent variable Inspirational Motivation is not directly observable since there is
no one dimension which can be used to measure it. However, theory (in this case
transformational leadership theory) proposes that where leaders demonstrate
high levels of Inspirational Motivation behaviour, then their subordinates will (a)
observe high frequencies of the four behaviours described in the statements and
(b) correspondingly, report high scores for each of the indicator variables.
Satisfactorily establishing the latent variables is the first stage in SEM analysis
and underpins the second (structural relations) stage where relationships between
latent variables are measured.