We translated the original English HEAS (Hogg et al., 2021) into German using the TRAPD approach (translation, review, adjudication, pre-test, documentation) as recommended by the European Social Survey (Dorer, 2018). First, three German native speakers fluent in English (SH, MS-H, and FP) independently translated the scale into German. Second, the three versions were discussed in the research team and integrated, yielding a pre-test version of the scale. Third, following the back-translation approach (Brislin, 1970), two researchers fluent in English (C2 level) and not involved in our study translated the scale back into English. Based on the back-translations, we made minor adjustments to the German pre-test version. Forth, we conducted a pilot survey with 33 participants to assess the comprehensibility of the scale. Given good comprehensibility of all items in the pilot survey, we did not apply further changes to the German HEAS. The English and German items of the HEAS are reported in Table 1. The protocol of the translation can be requested from the corresponding author.

We tested the German HEAS with 486 participants (121 male/357 female/8 diverse) in Germany (age M [SD] = 29.43 [10.63], median: 26 years, range: 18–73). To reach an adequate sample size for our planned analyses, we used three different recruitment approaches: 158 participants (students) were recruited via online advertisements and mailing-lists at 40 German universities (sample 1). One hundred and ninety-six participants (students and university staff) were recruited at Freie Universität Berlin via flyers, posters, and emails (sample 2) and 132 participants (students) at University of Potsdam via an online recruitment system for university students and online advertisement (sample 3). Using a link/QR code on the study invitation, participants accessed and completed an online survey implemented in the survey software Unipark (Version 21.2, QuestBack GmbH, Oslo, Norway).

We calculated Cronbach’s alpha for all HEAS subscales to estimate internal consistency. To explore concurrent and discriminant validity, we investigated associations with the DASS-21 and emotional reactions towards the climate crisis. Comparable to Hogg et al. (2021), we fitted a multiple linear regression model to assess unique associations between the DASS-21 anxiety subscale and each HEAS subscale while controlling for the remaining HEAS subscales. To test unique associations of emotional reactions with the HEAS affective symptoms subscale, we fitted a second multiple linear regression model. Furthermore, we calculated bivariate Pearson correlations between HEAS subscales and DASS-21 subscales as well as emotional reactions towards the climate crisis.

We performed a Bayesian confirmatory factor analysis (CFA) to examine the factorial structure of the German HEAS. Bayesian CFA, unlike conventional CFA, offers certain benefits: Bayesian CFA employs probabilistic methods to effectively estimate parameters even when sample sizes are modest, mitigating issues associated with statistical power and enhancing the robustness of findings. Another notable feature of Bayesian CFA is its capacity to incorporate existing knowledge or beliefs into the analysis through “informed priors.” This means that researchers can introduce relevant information about parameter values before analyzing the data. Such a priori knowledge enhances the precision of parameter estimates and refines the accuracy of model outcomes. Furthermore, Bayesian CFA offers a more versatile approach for modeling cross-loadings of items on latent factors. Unlike conventional CFA, which only allows for substantial loadings of items on their respective factors, Bayesian CFA accounts for the possibility that items may have subtle yet meaningful relationships with other factors (near-zero loadings). This permits a more nuanced understanding of the relationships between variables, resulting in a more comprehensive representation of the underlying constructs (Depaoli, 2021). These attributes collectively establish Bayesian CFA as a valuable analytical tool, extending researchers’ capabilities to address challenges posed by limited samples, to leverage existing knowledge, and to effectively model complex relationships within the data.

We chose Bayesian CFA to incorporate information from prior work including data about the factorial structure and item loadings reported by Hogg et al. (2021) in our analysis. Considering this knowledge in the estimation process enabled us to include pre-existing information about the model parameters and update these assumptions (Depaoli and van de Schoot, 2017). Even small to moderate samples are sufficient to obtain accurate results if, as in this case, there is prior knowledge (Depaoli and van de Schoot, 2017). Model fit was assessed using posterior predictive checks, which compared the observed data with the estimated model, i.e., the posterior predictive distribution (Muthén and Muthén, 2017).

The statistics program Mplus (version 8, Muthén and Muthén, 2017) produces a confidence interval for the posterior predictive checks, which, if they include zero indicate that the hypothesized model structure adequately fits the observed data. The posterior predictive (PP) value of p indicates the proportion of replicated data that exceeds the original data. Low PP values of p indicate poor fit. Models with values <0.10 should be rejected, whereas values around 0.5 indicate excellent model fit (Cain and Zhang, 2019).

We compared a four-factorial model in which the main loadings of the items on their hypothesized factors were specified to a four-factorial model in which near-zero cross-loadings of items from the three factors rumination, behavioral symptoms and anxiety about personal impact were allowed on the affective symptoms factor (Muthén and Asparouhov, 2012). We did this to account for the fact that in a principal component analysis by Hogg et al. (2021), the affective symptoms factor was found to explain 50% of the item variance. To evaluate the assumption of minor cross-loadings of items from the rumination, behavioral symptoms and anxiety about personal impact factor on affective symptoms, we checked the prior-posterior predictive (PPP) value of p (Asparouhov and Muthén, 2017). The PPP value of p differs from the PP value of p: The PPP value of p is suitable for testing whether the assumptions of near-zero priors with small variances hold. This way, individual parameters are tested rather than the fit of the overall model. If the PPP value of p is close to zero, the hypothesis that these cross-loadings are minor is rejected, which may indicate model misspecification. Any cross-loadings that are not minor would contradict the intended clear assignment of items to their respective factors. In addition, we compared the four-factorial solution to three-, two-and one-factorial models where rumination, behavioral symptoms and anxiety about personal impact were merged with the affective symptoms factor, respectively.

The reporting of the analyses follows the recommendations by Depaoli and van de Schoot (2017). The CFA was performed using Bayesian estimation in Mplus (version 8; Muthén and Muthén, 2017). Two Markov chains were implemented for each parameter. A Markov chain is a computational algorithm to iteratively approximate the model parameters. Its characteristics imply that each new parameter value is conditional only on the preceding one, irrespective of the entire history of the chain. Through numerous iterations, Markov chains gradually converge towards a more accurate approximation of the true parameter values. To assess chain convergence, the Gelman and Rubin convergence diagnostic (Gelman and Rubin, 1992a,b) was implemented as described in the Mplus manual with a stricter convergence criterion than the default setting (0.01 instead of 0.05). To establish stable calculations, we initiated a preliminary phase of 50,000 iterations (initial burn-in phase) without recording the results, followed by a fixed number of 50,000 iterations with recorded outcomes (postburn-in iterations). The Gelman and Rubin (1992a,b) diagnostic indicated that convergence was obtained with these fixed iterations for each of the two chains. Next, the trace plots for each model parameter were visually inspected. For each of the model parameters, both chains showed a constant mean and variance in the postburn-in portion of the chain. To further endorse convergence, we estimated the model again but with the number of burn-in and postburn-in iterations doubled (i.e., 200,000 iterations in total). Again, convergence was obtained and the model parameters were almost identical for all main factor loadings and factor covariances, i.e., the percent of relative deviation was less than 1%. However, this was not true for minor cross-loadings of items on the affective symptoms factor (see below). The magnitude of their factor loadings was substantially greater in the model with doubled iterations than in the original model, with a relative deviation of up to 300%. We therefore report the results of models with doubled iterations.

When implementing the informative priors for the main loadings of items on their respective factors, i.e., using the estimates from Table 5 in Hogg et al. (2021), we followed the recommendations by Mplus and assumed that they followed a normal distribution. As Hogg and colleagues did not provide variances for the factor loadings, we conducted sensitivity analyses with different variance priors (0.001, 0.01, 0.1, 1.0 and 10) to test the robustness of our findings. We relied on the Mplus default prior settings for error variances of items and the latent factor covariance matrix.

Recognizing the relatively infrequent use of Bayesian CFA, we also offer model fit indices of a conventional CFA to enhance interpretation. In evaluating model fit, we applied the following criteria: χ²/df ≤ 2, Comparative Fit Index (CFI; Bentler, 1990) ≥0.95, Tucker Lewis Index (TLI; Tucker and Lewis, 1973) ≥0.95, Root Mean Square Error of Approximation (RMSEA; Steiger, 1980) ≤0.05, and Standardized Root Mean Squared Residual (SRMR; Hu and Bentler, 1999) ≤0.08. However, since conventional CFA does not permit the modeling of near-zero loadings for items 5–13 on the affective symptoms factor, the Bayesian model is more complex and not entirely congruent with the four-factorial conventional CFA.

The HEAS subscales affective symptoms (M [SD] = 0.69 [0.60]), rumination (M [SD] = 0.60 [0.67]), and anxiety about personal impact (M [SD] = 1.20 [0.70]) showed good internal consistency (Cronbach’s alphas = 0.83; 0.86; 0.83, respectively). The internal consistency of the subscale behavioral symptoms (M [SD] = 0.33 [0.50]) was acceptable (Cronbach’s alpha = 0.71).

Overall, model fit was best for the four-factorial model with variance priors of 0.1 (results for models with different variance priors are available upon request). The model fit was acceptable based on a PP value of p of 0.187, and the four-factorial model showed better fit than the three-, two-, and one-factorial solutions where items loaded onto the affective symptoms factor instead of their content-specific factors. Furthermore, the Bayesian posterior predictive checking utilized χ² likelihood ratio tests to compare the observed-data test statistic with the replicated-data test statistic. Since its 95% confidence interval included zero, this result indicated that there was no significant difference between the observed-data χ² values and the replicated-data χ² values. Finally, the PPP value of p of 0.902 was excellent and suggested that the assumption of near-zero cross-loadings in the four-factorial model was valid. The findings are presented in Table 2.

Model fit indices from conventional frequentist CFA support the conclusion of good model fit with exception for the χ² value: χ²/df = 2.45 (144.47/59), p ≤ 0.001, CFI = 0.983, TLI = 0.977, RMSEA = 0.055 (90% CI, 0.043–0.066), and SRMR = 0.024.

Table 3 displays the factor loadings of items in the four-factorial model with minor cross-loadings of items from the rumination, behavioral symptoms and anxiety about personal impact factor on the affective symptoms factor.

The intercorrelations of the latent factors were high. Affective symptoms correlated with rumination (0.79), behavioral symptoms (0.74), and anxiety about personal impact (0.65). Further correlations were: rumination with behavioral symptoms (0.55) and anxiety about personal impact (0.61); behavioral symptoms with anxiety about personal impact (0.43).

To examine the effects of informed priors for factor loadings on model estimates, we compared the results of the four-factorial model with informed priors with the model parameters that resulted based on diffuse priors for factor loadings with normal distribution. Differences in main factor loadings and factor covariances were, according to Depaoli and van de Schoot (2017), moderate (1–10%). But the levels of deviation were larger for the cross-loadings of all items on the affective symptoms factor although their model parameters were modeled as diffuse in both analyses. In the alternative model without informed priors, particularly the items 7 (“Unable to stop thinking about losses to the environment”), 9 (“Difficulty enjoying social situations with family and friends”), and 13 (“Feeling anxious that your personal behaviors will do little to help fix the problem”) had stronger than near-zero (>0.1) loadings on the affective symptoms factor, with l₇ = 0.16, l₉ = 0.19, and l₁₃ = 0.11. Thus, prior assumptions about factor loadings slightly affected the analyses but the conclusions regarding the number and structure of factors remained unchanged.

Scores of the DASS-21 depression (n = 158, M[SD] = 4.97 [4.41]), anxiety (3.01 [3.67]), and stress subscales (6.32 [4.32]) were below clinical thresholds. A multiple regression model investigating unique associations of each HEAS subscale and the DASS-21 anxiety subscale showed that the affective symptoms subscale (standardized β = 0.29, p = 0.011) and the behavioral symptoms subscale (standardized β = 0.25, p = 0.009) were significantly associated. Bivariate correlations between all HEAS subscales and all DASS-21 subscales are reported in Table 4.

When entering all 18 emotional reactions towards the climate crisis into the multiple linear regression model to test unique relationships with the HEAS affective symptoms subscale, only the emotions “anxious” (standardized β = 0.19, p < 0.001), “desperate” (standardized β = 0.19, p = 0.001), and “hurt” (standardized β = 0.19, p < 0.001) were significantly related when controlling for all other emotions. See Table 4 for bivariate correlations between all HEAS subscales and emotional reactions.

Some limitations need to be considered when interpreting our results. First, the study samples were not representative for the general population given that large proportions of the sample were young, female and highly educated which is due to recruitment in university settings. Thus, future research should be based on representative samples to assess whether our results can be generalized to the German population. Second, while we were able to investigate several important psychometric properties of the German HEAS in this study, other properties such as test–retest reliability remain to be investigated in future studies (Mokkink et al., 2010).

Finally, given the confirmatory approach of the current study, other possible conceptions of eco-anxiety were not investigated. As suggested by Hogg et al. (2021), eco-anxiety may appear differently in groups or societies already more strongly affected by the negative consequences of the climate and environmental crises, highlighting the need for further research on eco-anxiety in the Global South, indigenous people and other exposed populations such as farmers. Moreover, future work should investigate the overlap between eco-anxiety and related emotions including, but not limited to, the anxiety of societal impacts on the environment - as opposed to personal impacts - as well as frustration and anger about a lack of effective policies.

The German translation of the HEAS was tested in a sample of 486 participants in Germany and the scale and its subscales were found to be as reliable as the original English version. The Bayesian CFA confirmed the multidimensionality of the construct supporting a four-factorial model of eco-anxiety (affective symptoms, rumination, behavioral symptoms, anxiety about personal impact). Regression results and weak to moderate associations between the HEAS subscales and the DASS-21 subscales indicate that eco-anxiety is distinct from general depression, anxiety, and stress, but shares a significant proportion of variance. Taken together, the study suggests that the German HEAS is a reliable and valid scale to measure eco-anxiety.