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In Pursuit of Eco-innovation
about the distributions of variables, these same factors can be expected
to influence evaluation of model fit (Hu and Bentler 1995). In our study,
we report the values of χ2 tests notwithstanding that these are high and
consistently statistically significant, which is the result of the influence
exerted by the sample size – performing more poorly in smaller samples
that are considered to be not “asymptotic” enough. In addition, some oth-
er fit indexes, such as NFI, perform more poorly when they have a small
sample size. Therefore, Bearden, Sharma and Teel (1982 cited in Hu and
Bentler 1995) found that the mean of NFI is positively related to sample
size and that NFI values tend to be far less than 1.00 when sample size
is small (NFI is therefore not a good indicator for evaluating model fit
when N is small).
In our study, we will report the following fit indexes:
144 - Chi-square (χ2 test) – the fundamental measure used in SEM to
quantify the differences between the observed and estimated co-
variance matrices. Chi-square is influenced by the difference in
covariance matrices and by sample size. Moreover, increasing the
size of the covariance matrix (i.e., using more indicator variables)
increases the chance that the differences in matrices will be lar-
ge (i.e., significant p-values can be expected). In SEM, we do not
want the p-value for the χ2 test to be small (statistically signifi-
cant). Rather, if our theory is to be supported by this test, we
want a small χ2 value (and corresponding large p-value), thus in-
dicating no statistically significant difference between the matri-
ces (meaning that the observed sample and SEM estimated co-
variance matrices are equal and the model fits perfectly) (Hair et
al. 2009).
- SRMR (Standardized Root Mean Square Residual) – an alter-
native statistic based on the residuals is the standardized root
mean residual, which is a standardized value of RMSR and thus
is more useful for comparing fit across models. Lower SRMR
values represent better fit and higher values represent worse fit,
which puts the SRMR into a category of indexes sometimes
known as badness-of-fit measures, in which high values are in-
dicative of poor fit (Hair et al. 2009). The average SRMR value
is 0, meaning that both positive and negative residuals can oc-
cur. Thus, a predicted covariance lower than the observed value
results in a positive residual, while a predicted covariance larger
than the observed value results in a negative residual. It is diffi-
cult to provide a hard-and-fast rule indicating when a residual is
about the distributions of variables, these same factors can be expected
to influence evaluation of model fit (Hu and Bentler 1995). In our study,
we report the values of χ2 tests notwithstanding that these are high and
consistently statistically significant, which is the result of the influence
exerted by the sample size – performing more poorly in smaller samples
that are considered to be not “asymptotic” enough. In addition, some oth-
er fit indexes, such as NFI, perform more poorly when they have a small
sample size. Therefore, Bearden, Sharma and Teel (1982 cited in Hu and
Bentler 1995) found that the mean of NFI is positively related to sample
size and that NFI values tend to be far less than 1.00 when sample size
is small (NFI is therefore not a good indicator for evaluating model fit
when N is small).
In our study, we will report the following fit indexes:
144 - Chi-square (χ2 test) – the fundamental measure used in SEM to
quantify the differences between the observed and estimated co-
variance matrices. Chi-square is influenced by the difference in
covariance matrices and by sample size. Moreover, increasing the
size of the covariance matrix (i.e., using more indicator variables)
increases the chance that the differences in matrices will be lar-
ge (i.e., significant p-values can be expected). In SEM, we do not
want the p-value for the χ2 test to be small (statistically signifi-
cant). Rather, if our theory is to be supported by this test, we
want a small χ2 value (and corresponding large p-value), thus in-
dicating no statistically significant difference between the matri-
ces (meaning that the observed sample and SEM estimated co-
variance matrices are equal and the model fits perfectly) (Hair et
al. 2009).
- SRMR (Standardized Root Mean Square Residual) – an alter-
native statistic based on the residuals is the standardized root
mean residual, which is a standardized value of RMSR and thus
is more useful for comparing fit across models. Lower SRMR
values represent better fit and higher values represent worse fit,
which puts the SRMR into a category of indexes sometimes
known as badness-of-fit measures, in which high values are in-
dicative of poor fit (Hair et al. 2009). The average SRMR value
is 0, meaning that both positive and negative residuals can oc-
cur. Thus, a predicted covariance lower than the observed value
results in a positive residual, while a predicted covariance larger
than the observed value results in a negative residual. It is diffi-
cult to provide a hard-and-fast rule indicating when a residual is
