leadership and motivation in hospitality

Cross-checking the imputation method

As described above in Section 6.6.1, the AMOS software provides a special form
of maximum likelihood (full information maximum likelihood, FIML) estimation to
compute model parameters where variables contain missing data (Kline 2005: 56;
Arbuckle 2009: 270). The FIML method, however, does not allow for the
computation of a standardised residual covariance matrix (SRCM) or modification
indices (MIs) and is therefore not appropriate for model development processes,
where the SRCM and MI estimates provide essential information for evaluating
levels of shared unmeasured covariance between indicator variables.

Accordingly, the model-based imputation method (also provided by AMOS and
which does allow for estimation of modification indices) was used for the model
development process. Shumaker and Lomax (2004: 43) note that it ‘is prudent’
for researchers to cross-check SE models that have been estimated using data
imputation with AMOS’s Full Information Maximum Likelihood (FIML) method.

Model 5b was therefore re-estimated using the FIML approach. The model fit
estimates (Table 7 - 32 ) indicate that there is no significant difference in model fit
between the model developed using the imputed data set and the same model
estimates using the FIML method. Six of the thirteen standardised factor loadings
differed between models by 0.001 and one differed by 0.003; of the five
standardised structural coefficients, two varied between models with differences
of 0.001, one had a difference of 0.002 and one had a difference of 0.003.
Essentially, there was no substantial difference in magnitudes of parameter
estimates and all parameter estimates remained statistically significant.

Fit measure Model-based

data imputation

method

FIML method

No missing

values

n = 177

χ^2 (d.f.; p) 116.829 (98;

0.094)

115.758 (98;

0.106)

111.333 (98;

0.169)

RMSEA

(upper; lower;

pclose)

0.030

(0.049; 0.000;

0.959)

0.029

(0.048; 0.000;

0.964)

0.028

(0.050; 0.000;

0.948)

CFI 0.991 0.991 0.992

SRMR 0.0559 N/a(a) 0.0617

Hoelter’s Critical N 222 224 194

(a) SRMR is not defined in AMOS where missing values are present

Table 7-32 Post-development comparisons for Model 5b