to be fairly robust with the data that violate multivariate normality (Bollen & Long,
1993). Finally, this study replaces missing values with the mean values of each variable
based on valid responses because SEM is sensitive to the presence of missing variables.
Analytic Procedures for SEM
To assure that both models are properly specified, it is critical to follow the three
steps of SEM: (a) identify a proposed model, (b) evaluate the model fit, and (c) modify
the model if the original model fit is bad.
A Proposed model
First, SEM begins with what is a conceptual rather that a statistical component:
causal model. Therefore, based on previous literature and prior discussions, a reading
model was proposed. In general, the models were established through three distinct
phases. First, a measurement model confirmed the validity of the constructs that were
used in later structural models. The purpose of this model was to identify the constructs
with reduced error variance, and the constructs could be established by a factor analysis.
Second, a predictive structural model was created to test the direct effects of multiple
predictors on reading. Third, a mediated reading model was structured to test hypotheses.
Figure 3-1 presents the model for this study that includes three factors that can be related
to reading levels. A causal model is a hypothesis about the field of variables that affect
one or more dependent variables of interest, presented formally as a path diagram. The
diagram in Figure 3-1 demonstrates that early elementary children's level of reading is
correlated with phonological awareness, rapid-naming, and visual skills. The model was
overidentified to meet basic requirement for model identification. In other words, the
number of parameters must be less than the number of observations. The overidentified
model resulted in positive degrees of freedom, which allowed for the rejection of the