STABILITY AND CHANGE IN RISK-TAKING PROPENSITY
Supplemental Materials
Stability and Change in Risk-Taking Propensity Across the Adult Lifespan
by A. K. Josef et al., 2015, Journal of Personality and Social Psychology
A. Dimensionality of Risk-Taking Propensity
To examine the dimensionality of the risk-taking propensity items used, we first computed Pearson correlations between the different domains in each wave (2004, 2009, and 2014). The results showed that the correlational pattern between the risk domains is similar in the different waves, and that there seems to be a substantial amount of common variance between risk-taking propensity ratings in the different domains (r = .31–.59; see Tables S1–3 below). Lowest intercorrelations emerged between social risk-taking propensity and the other domains of risk.
Table S1
Correlations Between General and Domain-Specific Self-Reported Risk Propensityin 2004
G / D / F / R / O / HG
D / .46
F / .48 / .49
R / .53 / .53 / .48
O / .59 / .48 / .47 / .59
H / .45 / .48 / .42 / .50 / .52
S / .39 / .31 / .37 / .37 / .39 / .42
Note. G = general risk, D = driving risk, F = financial risk, R = recreational risk, O = occupational risk, H = health risk, S = social risk. M = mean correlations of risk item listed in column with all other risk domains. N = 11,567. All correlations are significant at p < .001.
Table S2
Correlations Between General and Domain-Specific Self-Reported Risk Propensityin 2009
G / D / F / R / O / HG
D / .52
F / .49 / .47
R / .51 / .56 / .46
O / .51 / .48 / .42 / .58
H / .47 / .50 / .43 / .51 / .52
S / .37 / .29 / .35 / .33 / .36 / .39
Table S3
Correlations Between General and Domain-Specific Self-Reported Risk Propensityin 2014
G / D / F / R / O / HG
D / .44
F / .43 / .47
R / .46 / .55 / .46
O / .47 / .47 / .44 / .58
H / .39 / .48 / .45 / .51 / .51
S / .32 / .31 / .38 / .34 / .36 / .41
Second, we conducted exploratory and confirmatory factor analyses (averaged for the three years). The exploratory analysis yielded eigenvalues, suggesting that a single factor explained most (54%) of the variance (with all other factors below 10% of explained variance; see Figure S1). The confirmatory factor analysis confirmed this conclusion in showing that a one-dimensional model fit the data well (CFI = 0.980, RMSEA = 0.059; SRMSR = 0.023). Social risk taking again showed to have the lowest loadings on a global risk factor relative to the other domains (see Table S4).
Figure S1. Eigenvalues of exploratory factor analysis averaged across the three waves.
Table S4
Cross-Sectional Correlations and Factor Loadings of Risk Taking Propensity Ratings Across Domains
G / D / F / R / O / H / Factor LoadingG / .70
D / .47 / .69
F / .48 / .47 / .65
R / .51 / .54 / .47 / .76
O / .53 / .48 / .45 / .59 / .74
H / .45 / .49 / .42 / .51 / .52 / .69
S / .37 / .30 / .36 / .35 / .37 / .41 / .51
Note. Values presented are based on results averaged for the three waves. Correlations were significant at p < .001. G = general risk, D = driving risk, F = financial risk, R = recreational risk, O = occupational risk, H = health risk, S = social risk. Fit measures for confirmatory factor analysis CFI = .980, RMSEA = .059, SRMR = 0.023. Factor loadings represent standardized values.
B. Change of Risk-Taking Propensity Factor Across the Life Span
Measurement Invariance
In order to evaluate measurement invariance of risk-taking propensity measured by seven items, we conducted a series of analyses. First, we tested a baseline model (configural invariance) in which all parameters (e.g. factor loadings and item intercepts) were freely estimated over time (2004, 2009, and 2014). Seven items measured risk-taking propensity at each measurement point. The items were allowed to load on one latent variable in each year. The variance of each latent variable was fixed to 1. Item loadings and correlations between the latent variables were freely estimated. Second, we tested for metric invariance by constraining factor loadings of the items to be equal in each year of measurement. Latent variable variance for the years 2009 and 2014 was freely estimated. If this constraint improves model fit, then the items are connected to the latent variable in the same way each year. Third, we restricted the model such that it tested scalar invariance by constraining the intercepts of each item to be the same over time. We freely estimated the latent mean in the years 2009 and 2014 and fixed the intercept in 2004 to 0. Like this, the estimated means in 2009 and 2014 can be interpreted as changes relative to 2004. This ensures that observed values on each latent variable have the same meaning.
Table S5
Model Fits for Invariance Models
X2 / df / RMSEA / CFI / SRMRModel 1
Configural invariance / 19745.711 / 189 / 0.093 / 0.804 / 0.123
Model 2
Metric invariance / 19524.917 / 199 / 0.647 / 0.806 / 0.113
Model 3
Scalar invariance / 20045.178 / 209 / 0.089 / 0.801 / 0.144
Table S5 shows the fit indexes of the increasingly restrictive models. Model 3, which tested scalar invariance in risk-taking propensity as measured by six items, showed to have best model fit.
Latent Growth Curve Modeling
Table S6 and Figure S2 show the effect of age and sex on mean level (intercept) and mean-level change (slope) as measured by a latent growth model. All model parameters were standardized relative to the first measurement, and therefore the mean of the intercept was set to 0, and its variance set to 1. Overall, both age and sex had a significant effect on mean-level risk-taking propensity, with considerable declines in risk-taking propensity across the whole adult life span. Steepest declines are evident from about sixty years of age. Concerning sex, males consistently reported higher levels of risk-taking propensity relative to females. Age and sex also significantly influence how individuals change over time. More concretely, individuals show a stable decrease in risk-taking propensity across the adult life span. Decline in females, however, is less pronounced relative to males.
Table S6
Latent Growth Curve Models
Risk TakingN = 11,903
Model fit
X2 (df) / 19742.292 (286)
CFI / 0.812
RMSEA / 0.076
SRMR / 0.054
b / p
Intercept
Age / −0.291
[0.020] / <.001
Age2 / −0.031
[0.006] / <.001
Age3 / −0.015
[0.004] / .001
Sex / −0.835
[0.029] / <.001
Slope
Mean / −0.143
[0.014] / <.001
Age / −0.014
[0.013] / .280
Age2
Age3
Sex / 0.097
[0.034] / .004
Note. Model parameters were standardized relative to the first measurement (i.e., the mean of the intercept was set to 0, and the variance was set to 1). Models contain higher-order terms of age only if they were significant at age < .05. Values for age are given in 10-year units. CFI = comparative model fit; RMSEA = root-mean-square error approximation; SRMR = standardized root-mean-square residual.
Figure S2. Mean-level (intercept), mean-level change (slope) and a combined display of cross-sectional and longitudinal changes in risk-taking propensity as measured by seven domain-specific risk items.
C. Longitudinal Change in Risk-Taking Propensity for Different Age Cohorts
We conducted additional analyses on the raw data to investigate the pattern of change for different cohorts and to diagnose potential discrepancies between predicted trajectories of the latent growth curve models and the raw data.
More concretely, for respondents of all ages (by year) in our longitudinal samples, we looked at changes in risk-taking propensity between two time points two (domain-general risk-taking propensity) or five years (domain-specific risk-taking propensity) apart and plotted the means for five-year cohorts (see Figure S3). The results show that, overall, the pattern matches the results obtained from the latent growth curve models (Figure 3 in the manuscript). Yet, in very old ages, it is evident that the pattern of change becomes noisier relative to the rest of the age range, possibly due to smaller numbers of respondents in these age groups. This is in line with our observations that for some risk domains, cross-sectional and longitudinal changes diverge (see Figure 3 in the manuscript, intercept + slope, model-implied), possibly due to cohort differences or attrition effects of respondents of very old ages.
Figure S3. Mean-level changes in risk-taking propensity across the life span for separate 5-year cohorts.
D. Latent Moderated Regression Model
To analyze rank-order stability of risk-taking propensity over five years on the latent level, we set up a latent moderated structural equation model in Mplus (LMS, Klein & Moosbrugger, 2000). In this model, latent risk-taking propensity is measured by seven items (general, driving, financial, recreational, occupational, health, and social risk-taking propensity) at two time points. The first time point serves as an independent variable, and the second time point as a dependent variable. Latent stability between the time points is measured via the standardized effect of t1 on t2. We further included the effects of age, age2, age3 and sex as moderators to assess their effects on latent stability of risk-taking propensity. More concretely, we predicted t2 with measurements at t1 and included the moderators as well as the interaction terms of the moderators and t1. Significant effects on the interaction terms illustrate that individuals change differently in risk-taking propensity over time. Factor loadings, measurement intercepts, and error variances were constrained to be equal across time. Because risk-taking propensity was measured by all seven items on three time points (2004, 2009, 2014), we set up three separate LMS to estimate the moderation of age and sex on stability of risk-taking propensity levels between two five-year intervals (2004–2009, 2009–2014) and one ten-year interval (2004–2014).
We adhered to a two-step estimation process for LMS models (see Maslowsky, Jager, & Hemken, 2014). First, we estimated the model without the interaction terms (Model 0). This model provided model fit indices. Second, we estimated the model with interaction terms between T1 and age, age2, and age3 (Model 1). The output of Model 1 provides the final regression coefficients and shows whether the interaction terms are significant. Since Mplus does not provide standardized regression coefficients for LMS models, we standardized the data prior to data analysis.
The results show that age and sex significantly influenced rank order stability of risk-taking propensity (see Table S7). The results are similar to those observed for the analyses reported for the separate domains in the main paper. Please note, however, that the model fit indices (CFI, RMSEA, SRMR) are not very good, indicating that a separate investigation of stability in different life domains may be reasonable.
Table S7
Latent Stability Over Two Five-Year Intervals and One Ten-Year Interval
2004–2009 / 2009–2014 / 2004–2014CFI / .221 / .180 / .175
RMSEA / .336 / .335 / .335
SRMR / .164 / .163 / 162
b / p / b / p / b / p
Mean / .55 / <.001 / .64 / .010 / .54 / <.001
Age / .026 / .014 / .030 / .006 / .035 / .005
Age2 / −.017 / .102 / −.018 / .043 / −.041 / <.001
Female / −.030 / .184 / −.014 / .001 / −.014 / .217
Note. Age was centered to the sample mean. Values for age are given in 10-year units. CFI = comparative model fit; RMSEA = root-mean-square error approximation; SRMR = standardized root-mean-square residual.
Figure S4. Latent stability of risk-taking propensity over two five-year intervals and one ten-year interval.
Figure S5. Self-report item on domain-general risk propensity.
English translation:
“Are you generally a person who is willing to take risks or do you try to avoid taking risks? Please tick a box on the scale, where the value 0 means not at all willing to take risks and the value 10 means very willing to take risks."
Figure S6. Self-report item on domain-specific risk propensity.
English translation:
“People can behave differently in different situations? How would you rate your willingness to take risks in the following areas? Please tick a box on the scale, where the value 0 means not at all willing to take risks and the value 10 means very willing to take risks."
How is your willingness to take risks…
…while driving?
…in financial matters?
…during leisure and sport?
…in business and professional matters?
…in health-related issues?
…when trusting other people?