Univariate outliers are cases with extreme values on one variable whereas
multivariate outliers have extreme scores on two or more variables. It is possible
to identify multivariate outliers by checking for extreme Malahanobis distance D^2
values (Byrne 2010: 105-106) and also using the associated p values, where
p<0.001 signals a potential multivariate outlier (Kline 2005: 51 - 52). Using this
method, four outliers were identified and removed (case numbers 193, 68, 158
and 58 – details are provided in Appendix IV).
The measurement model is now re-estimated (CFA 5:8) with 209 cases.
CFA 5:8 achieves discriminant validity: the lowest AVE (EM = 0.612) now exceeds
the highest squared correlation estimate (EPA EM = 0.555).
In addition, model fit has improved: χ^2 = 179.311, d.f. = 155, sig = 0.088;
RMSEA = 0.027 (0.044; 0.000; pclose = 0.992); CFI = 0.990; SRMR = 0.0413;
and CN (0.05) = 215. All factor loadings are satisfactory and statistically
significant and all parameters are robust to multivariate non-normality (see
Appendix IV).
Following the structural specification illustrated in Figure 7 - 19 and the
measurement model specification described in Table 7 - 26 , SEM 5:1 is estimated
using 209 cases. There are two issues with SEM 5:1. Firstly, the structural path
WV→EPA is not statistically significant. Secondly, the model χ^2 p value is 0.025,
that is, it is below the 0.05 threshold for model χ^2 and indicates that the model
does not fit the data well.
An examination of the standardised residual covariance matrix (SRCM) reveals the
source of this problem: the SRC value for WV6/JP1 is above the 2.58 threshold
(see Section 7.2.8). Looking to the diagnostic information to identify which of
these two indicators is the weaker performing one, we see that WV6 has a factor
loading of 0.824 and JP1 has a factor loading of 0.900 and, in the standardised
residual covariance matrix, WV6 has a higher level of associated unmeasured
variance compared with JP1 (30.2 versus 21.1). Accordingly, WV6 is removed
and the model re-estimated. Firstly, a modified CFA model (without WV6) is
estimated to ensure that convergent and discriminant validity are maintained.
This revised CFA model continues to satisfy the criteria for construct validity and
also demonstrates an improved model fit – importantly, the model χ^2 p value is
now >0.05 (χ^2 = 148.259, d.f. = 137, sig = 0.241; RMSEA = 0.020 (0.040; 0.00;
pclose = 0.997); CFI = 0.995; SRMR = 0.0398; and CN (0.05) = 231).