The LIFE-Adult-Study, conducted by the Leipzig Center for Civilization Diseases (LIFE), is a population-based study with a representative sample of residents from Leipzig, Germany, a city with a population of about 550,000. An age- and gender- stratified random selection of inhabitants was obtained from the local residents’ registration office. The age range was 18 to 80 years. According to the study protocol, the focus was on the age group 40-80 years; the 18-39 years age range was included but underrepresented. At the study center, the participants underwent a set of assessment batteries, including collection of their sociodemographic data, medical history, lifestyle factors, and several medical examinations. Pregnancy and insufficient command of the German language were exclusion criteria. The participants received a lump sum of 20 EUR to cover their travel expenses. Details of the study design are published elsewhere (Loeffler et al., 2015). Informed consent was obtained from all participants. The study was approved by the ethics committee of the University of Leipzig.

The LOT-R (Scheier et al., 1994) is composed of 10 items. Three items assess optimism, three items assess pessimism, and there are four filler items. Respondents are asked to indicate the degree to which they agree with the items on a five-point Likert scale (cf. Hartley, 2014). The scores of the Optimism and Pessimism subscales are calculated by summing up the corresponding three items, resulting in a score range of 0 to 12. The total sum score is calculated by adding the optimism score and the inverted pessimism score. Sociodemographic factors were obtained in a structured interview. Alcohol consumption was assessed with regard to frequency and amount of different alcoholic beverages consumed within the last year, and tobacco use with questions on past and current smoking, smoking duration, and amounts of different tobacco products.

Age and gender differences were tested with a two-factorial ANOVA, using the factors age group (5 categories according to Table 1) and gender (2 categories). Cronbach's alpha coefficient was used to determine internal consistency. Effect sizes were calculated using Cohen's d, relating the mean score differences to the pooled standard deviation. Percentile rank scores were defined in the same way as in the previous German normative study (Glaesmer et al., 2012): percentile rank=(m+0.5 k)/N * 100, where m is the number of members of the sample obtaining a score lower than the score of interest, k is the number obtaining the score of interest, and N is the overall sample size. Logistic regression analyses were performed to quantify the effect of socioeconomic status, education, professional status, alcohol consumption, tobacco smoking, and obesity on the LOT-R scores, adjusting for age and gender. The calculations were performed with SPSS version 20.

The factorial structure was tested with Confirmatory Factor Analyses (CFA), performed with AMOS 20. All models were calculated using covariance matrices, and each model was estimated with the maximum likelihood method approach. All models were compared to each other on the basis of the following model fit indices: minimum discrepancy divided by its degrees of freedom (CMIN/DF), normed fit index (NFI), comparative fit index (CFI), Tucker-Lewis Index (TLI), root mean square error of approximation (RMSEA), standardized root mean square residual (SRMR), and Bayesian Information Criterion (BIC). For a good model fit, the ratio CMIN/DF should be as small as possible (Schermelleh-Engel, Moosbrugger, & Müller, 2003); values of NFI, CFI and TLI close to .95 or higher are indicative of a good or at least acceptable (>.90) model fit. Furthermore, RMSEA should be .08 or smaller, and SRMR should be .05 or smaller. The BIC is a descriptive indicator of poor fit for the comparison between two models; the model with the lower BIC should be preferred (Schermelleh-Engel et al., 2003).

To test the invariance of the model across gender and age, further analyses were conducted using multi-group CFA. After testing the factorial structure in each subgroup, measurement invariance was tested in three steps: first using the configural model (no constraints), followed by a metric invariant model (with unstandardized item loadings constrained to be equal across groups), and finally a scalar invariant model (with unstandardized item loadings and unstandardized item intercepts simultaneously constrained to be equal across groups). Based on the hierarchy of these nested and increasingly restrictive models, the models were then compared to each other. Since the χ2 statistic has been criticized for its sensitivity to sample size, we focused mainly on the differences ΔCFI and ΔRMSEA. Values smaller than .01 indicate the invariance of the models (Cheung & Rensvold, 2002). For scaling purposes, the variance of each latent variable was fixed to 1.0 and the mean was fixed to 0 to avoid the potential problem of selecting a marker variable that may not be invariant.

The total sample of the study program comprised 10,000 people from the general population. The response rate of the study was 33%. Further details of the sampling procedure are reported elsewhere (Loeffler et al., 2015). If only one item of a subscale (Optimism or Pessimism) was missing, it was replaced with the rounded mean of the other two items. Following this procedure, valid data were available for 9,711 persons. Table 1 presents the sociodemographic characteristics of this sample.

Males were slightly less optimistic (M=8.6) than females (M=8.9), effect size d=.12, but there were no gender differences in pessimism (Table 2). Pessimism increased with increasing age for males and females. The ANOVA results for the effects of gender and age group on optimism and pessimism were as follows: Optimism: Gender: F=10.2, p=.001; Age group: F=4.4, p=.002; Gender * Age group: F=.84, p=.494; Pessimism: Gender: F=.73, p=.394; Age group: F=26.4, p<.001; Gender * Age group: F=2.2, p=.066; Total score: Gender: F=6.9, p=.009; Age group: F=20.9, p<.001; Gender * Age group: F=1.75, p=.137.

The reliability coefficients were: Optimism: alpha=.70; Pessimism: alpha=.63, and Total score: alpha=.66. The correlation between Optimism and Pessimism was calculated for several subgroups of the sample, concerning gender, age group, and education. For the total sample the correlation was r=-.22. Separated by gender, the correlations were r=-.21 (males) and r=-.24 (females). The age groups yielded the following results: r=-.50 (≤ 39 y.), r=-.40 (40-49 y.), r=-.31 (50-59 y.), r=-.12 (60-69 y.), and r=.05 (≥ 70 y.). Concerning education (in years), the correlations were r=.13 (< 10 y.), r=-.17 (10-11 y.), and r=-.38 (≥ 12 y.). The percentile rank scores of the LOT-R are listed in Table 3.

Factor models were tested with CFA according to the study of Cano-García et al. (2015). In that study seven models were tested, but models 3 and 4 were identical, so we calculated six models. Model 1 (one-factor model) is the unidimensional model of the LOT-R. Model 2 is a two-factor model (optimism and pessimism) with both latent variables correlated with each other. In this model, the positive items load onto one factor, and the negative items load onto the other. Model 3 also considers two factors (optimism and pessimism), but these factors are assumed to be uncorrelated. In Model 4 the three pessimism items are combined by a methods factor. Accordingly, in Model 5 the methods factor is related to the three optimism items. Model 6 is the “random intercept factor model” according to Maydeu-Olivares and Coffman (2006). It includes a method factor in addition to a unidimensional model of the LOT-R. Within this model, the intercepts of the method factor are allowed to vary freely across the individuals.Fit indices are given in Table 4. While models 1 and 3 showed insufficient model fit, the remaining four models (2, 4, 5, and 6) are characterized by very similar and good model fit coefficients. Among these four models we preferred the most parsimonious model (Model 2) for further analysis of measurement invariance. Empirical data support the assumption of a bi-dimensional factor structure of the LOT-R, with two latent factors that correlate with r=-.35. Standardized factor loadings of the latent variables on the related items varied between .56 and .76 for the optimism subscale and between .48 and .72 for the pessimism subscale.

The invariance of the preferred model (Model 2) was tested across the subgroups of men and women and five age groups. Results of the measurement invariance tests are shown in Table 5. As the indices of ΔCFI and ΔRMSEA indicate (<.01), this model can be assumed to be metric invariant across gender and age groups. Due to ΔCFI>.02, scalar invariance could not be confirmed completely across men and women and all age groups. According to Gregorich (2006), the constraint of equal intercepts was freed for item 6 (invariance test for gender) and items 5 and 6 (invariance test for age) respectively, and the model was re-estimated for partial scalar invariance. As shown in Table 5, partial invariance across gender and all age groups could be confirmed. The Δχ2 statistic indicated significant differences in all cases of the invariance tests, but due to its sensitivity to sample size we focused on differences in RMSEA and CFI values (Schermelleh-Engel et al., 2003).

Low optimism (LOT-R total) scores were observed for people who were widowed (M=15.5), unemployed (M=14.2), had low levels of education (M=15.1), and had low income (M=15.1) (Table 6). The associations between the other factors (smoking, alcohol consumption and overweight) and optimism were lower; the influence of alcohol intake on optimism was negligible.