Testing the Assumption of Population Homogeneity in the Measurement of Dispositional Optimism: Factor Mixture Modeling Analysis

Abstract

The assumption of population homogeneity in the measurement of dispositional optimism was examined. U.S. and Canadian respondents (N = 591) completed an optimism scale. Possible population heterogeneity was analyzed using factor mixture modeling. Two major results emerged. First, population homogeneity was not supported: A large class of participants had trouble giving consistent answers to optimism items, optimism and pessimism items, or, especially, pessimism items. Second, after the removal of this problematic class, the correlation between optimism and pessimism was found to be .94, a magnitude large enough to support the assumption of unidimensionality. Although psychometric problems with the measurement of optimism have not been identified previously, this study suggests that the typical measurement of dispositional optimism requires substantial revision. The findings showcase the importance of factor mixture modeling in evaluating the psychometric properties of a measurement scale.

Appendix: Dispositional optimism items

op1: I’m optimistic about my future.

ps1: I’m pessimistic about my future.

(Original LOT–R item: I’m always optimistic about my future.)

op2: I expect things to go my way.

ps2: I expect things to go against my wishes.

(Original LOT–R item: I hardly ever expect things to go my way.)

op3: I count on good things happening to me.

ps3: I expect bad things to happen to me.

(Original LOT–R item: I rarely count on good things happening to me.)

op4: Overall, I expect more good things to happen to me than bad.

ps4: Overall, I expect more bad things to happen to me than good.

(Original LOT–R item: Overall, I expect more good things to happen to me than bad.)

Note. op = optimism; ps = pessimism; LOT–R = Life Orientation Test–Revised.

Notes

1 This article follows the customary practice in the multitrait–multimethod literature, which is to regard the use of opposite-keyed items as a different method of measuring the same construct.

2 Geiser, Burns, and Servera (2014) argued that it is important to test MI across different methods. This will provide additional insights into the psychometric properties of regular- and reverse-keyed items. In this work, optimism and pessimism items load on two separate latent factors. MI is tested between optimism items and pessimism items.

3 The choice of which item is fixed to have the factor loading of 1 and an item intercept of 0 is important, because this item will influence the mean score of its corresponding latent factor. See Litson et al. (2017) for a detailed explanation (cf. Kam & Fan, 2018). In this study, a pair of signature items (“I’m optimistic about my future” and “I’m pessimistic about my future”) was chosen to carry these specifications. The mean score of these two items will thus influence the mean of the optimism factor and the pessimism factor.

4 I also tested a one-factor model, and the fit was worse, χ²(16) = 227.46, p < .001, TLI = .72, CFI = .84, RMSEA [90% CI] = .15 [.13, .17], SRMR = .07.

5 FMM does not allow maintenance of class membership as (posterior) probability while changing the specification to the model. Therefore, I extracted class membership based on maximum (posterior) probability. This is probably acceptable when entropy is large (e.g., > .80).

Additional information

Funding

Preparation of this article was financially supported by a Multi-Year Research Grant (MYRG2018-00010-FED) from the University of Macau.