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Moreover, the standard deviation of the intercept across prefectures is significantly high (.28), which justifies the relevance of a random coefficient model.
Common intercept: test of a common intercept across study groups assuming a common slope (p > 0.05, accept the hypotheses having common intercept across the study groups).
We then estimated a second order regression of variation in the intercept across a set of period and cohort levels.
Common intercept: p-value for the test of a common intercept across study groups assuming a common slope.
Intercepts and slopes were allowed to vary between individuals and level 2 residual covariance (between the slope and intercept across all individuals) was estimated.
To best approximate the pRF sizes from these prior reports, the average slope and intercept across reports was used, though analyses using individual slopes and intercepts from each of the prior reports yielded qualitatively and statistically similar results.
Similar(52)
Afterwards, we assessed the metric invariance (which implies equal factor loadings across groups) and the scalar invariance (which implies both equal factor loadings and equal indicator intercepts across groups).
The third step involved adding equality constraints on the item intercepts across groups and represents "scalar invariance" (Model 3).
Inspection of modification indices revealed a complex, non-uniform pattern of differences in item intercepts across groups.
The measurement invariance was tested in three steps using the configural, combined model (no constraints), followed by a metric invariant model (with equal item loadings, that is, the paths and covariances were constrained to be equal), and a scalar invariant model (with equal item loadings and item intercepts across groups) [ 29].
With continuous items, scalar invariance refers to the equivalence of items intercepts across groups (and over time, if applicable) whereas, with ordinal items, it pertains to the equivalence of items thresholds, which are analogous to item difficulty in Item Response Theory [ 53].
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