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Chunk #24 — Considerations Regarding Re-Parameterized Models — Strengths and Weaknesses of Re-parameterized Equations

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Distinguishing ordinal and disordinal interactions.
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This strength leads, however, to a potential complication when interpreting results. Four outcomes of point and interval estimates might be considered: (a) disordinal interaction (i.e., Ĉ falling within the range of X1), with the entire CI for Ĉ falling within the observed (or potential) range of X1; (b) disordinal interaction, but with the CI for Ĉ falling partly outside the range of X1; (c) ordinal interaction (i.e., Ĉ falling outside the range of X1), but with the CI for Ĉ falling partly within the range of X1; and (d) ordinal interaction, with the CI for Ĉ falling completely outside the range of X1. Scenarios (a) and (d) allow clear interpretation: under (a), both point and interval estimates of Ĉ are consistent with the interaction being characterized as disordinal; under (d), both point and interval estimates of Ĉ are consistent with the interaction being characterized as ordinal. Scenarios (b) and (c) are more problematic for interpretation. Under (b), one might conclude that the interaction is disordinal in the sample, but an ordinal interaction in the population cannot be rejected. In turn,