Below we present relevant evidence addressing each of our 5 research questions. For most of the analyses, data from all seven studies were combined into a single file. The data from all seven studies is available at https://doi.org/https://doi.org/10.5061/dryad.3j9kd51tc. To address the question of whether threat and efficacy appraisals are malleable, we analyzed each study separately as well as the combined data set. Before merging the data sets, participants who failed the attention check questions were removed. Within each study, the dependent variables were transformed into z scores, to adjust for the fact that the studies varied in the number of scale points used and to adjust for any differences between studies in the grand mean.
Does PMT predict behavioral intentions in the context of climate change?
To evaluate the utility of PMT in the context of climate change, we ran a stepwise multiple regression on the full data set, see Table 2. Demographic variables (political orientation, ethnicity, gender, belief in climate change) were included in Step 1. In Step 2, we added the PMT variables: threat, efficacy, and the threat x efficacy interaction term. We also include the 3-way interaction of threat x efficacy x belief in climate change to evaluate whether belief in climate change moderated the effectiveness of PMT in predicting behavioral intentions.
The demographic variables significantly predicted 24.7% of the variance in behavioral intentions; all but ethnicity were significant (ethnicity was marginally significant). Liberals, people of color (marginally), women, and those who believed in climate change expressed higher behavioral intentions to take action on climate change.
When the PMT variables were included, the percent of variability explained nearly doubled to 45.6%, a significant increase. Ethnicity and gender became nonsignificant. Consistent with PMT, both threat and efficacy strongly predicted behavioral intentions. The two-way interaction between threat and efficacy and the three-way interaction between threat, efficacy, and climate change belief were also both significant and are discussed further below.
Does PMT predict behavioral intentions for both climate change deniers and acknowledgers?
We considered the possibility that climate change deniers might answer questions about efficacy by choosing the highest possible answers, as it is easy to solve a problem that does not exist. Indeed, there were 59 climate change deniers (out of 1184, 5%) who chose the highest value for all efficacy questions. However, the majority of climate change deniers used the whole scale and gave lower efficacy ratings on average than climate change acknowledgers (M = -0.455, vs M = 0.056, t(3759) = 16.072, p 
Table 2 provides regression equations run separately for climate change deniers (N = 1125) and acknowledgers (N = 2577). As above, including PMT variables increased the percent of variance explained by the regression equation substantially for both groups, and threat and efficacy strongly predicted behavioral intentions for both groups. The data suggest that PMT effectively predicts behavioral intentions even among those who deny that the threat exists. The 2-way interaction between threat and efficacy was significant for both deniers and acknowledgers, though the regression weights were in opposite directions (the meaning of this is explored in the description of a significant three-way interaction below).
Are the effects of threat and efficacy additive or multiplicative?
The interactions reported above test whether threat and efficacy have additional impact in unique combination, above and beyond their additive effects. When all participants were included, the 2-way threat by efficacy interaction and the 3-way threat by efficacy by belief in climate change interaction were both significant. When looking within deniers and acknowledgers, the threat by efficacy interaction was significant for both groups.
To depict these interactions, we recoded threat and efficacy into binary variables (high/low) via median splits. Figure 2 depicts the three-way interaction (which qualifies the two-way interactions). For climate change deniers, the impact of threat on behavioral intentions was stronger for those high in efficacy. Among climate change deniers, the high threat/high efficacy group was the only one whose mean behavioral intentions were above the grand mean of zero. For climate change acknowledgers, the impact of threat on behavioral intentions was weaker for those high in efficacy; the low threat/high efficacy group had a higher mean than would be predicted by an additive model. Among climate change acknowledgers, the low threat/low efficacy group was the only one whose mean behavioral intentions were below the grand mean of zero.
Three-way interaction between threat, efficacy, and climate change belief predicting behavioral intentions
It should be noted that these effects were quite small. For all participants, including the interaction terms increased R2 from 0.456 to 0.460 (an increase of 0.4% of the variance). Among deniers, including the threat by efficacy interaction term increased R2 from 0.422 to 0.430 (0.8% of variance), and among acknowledgers from 0.270 to 0.273 (0.3% of the variance).
Do collective threat and efficacy measures improve the model accuracy for a collective problem like climate change?
Because climate change is a collective problem, we explored whether measuring collective threat and efficacy, distinct from personal threat and efficacy, improved the PMT model. Table 3 presents correlations between the personal and collective versions of each model component for the whole sample, as well as separately for deniers and acknowledgers. For the whole sample, the correlations between personal and collective variables were high, ranging from 0.494 to 0.811. The threat variables were more highly correlated with each other than the efficacy variables, suggesting that the distinction between personal and collective threat is not as clear to participants as the distinction between personal and collective efficacy. The correlations were also consistently significantly higher for climate change deniers than acknowledgers.
We quantified the additional predictive value of adding collective variables through stepwise regression equations. We included climate change deniers and acknowledgers in the same analysis and also ran separate regressions for each. Demographic variables, personal threat, and personal efficacy were included in Step 1. In Step 2 we added collective threat and collective efficacy.Footnote 2 The dependent variable was again behavioral intention.
The full regression models can be seen in Table 4. In all three iterations of the model, adding collective-level variables led to a significant increase in adjusted R2 (p’s 
When the data were split by climate change belief, collective threat remained significant for both groups. However, collective efficacy did not predict behavioral intentions for deniers (p = 0.211), while it positively predicted behavioral intentions for acknowledgers.
We also contrasted the variance explained by regression equations that included only person-level variables, only collective-level variables, and both (see Table 5). Whether looking at the entire sample or split by climate change belief, the combination of personal and collective explained roughly the same percentage of variance as models that only included personal-level variables. In sum, collective-level variables predicted independent variance in behavioral intentions, but did not really improve overall model fit.
Can threat, efficacy, and behavioral intentions be shifted through climate messaging?
To evaluate the malleability of threat, efficacy, and behavioral intentions we pursued 2 strategies: we looked at the inferential statistics and effect sizes in each study separately, and also used the combined data set of all seven experiments.
Results of individual studies
For each experiment, we conducted a series of 2-way ANCOVAs evaluating the impact of various messaging (condition) on climate change deniers and acknowledgers. Dependent variables were threat, efficacy, and behavioral intentions. In all analyses we controlled for ethnic identity, gender, and political leaning. A complete summary of the results for each study can be found in Additional file 1.
We found results at least partially consistent with our hypothesized effects for Study 1 (efficacy and behavioral intentions were higher in response to a message about air quality recovery during the COVID lock-down); Study 3 (White participants who read about racial disparities of climate impacts had lower behavioral intentions); Study 4 (efficacy and behavioral intentions were higher for those who read about scientists’ accurate predictions about COVID or climate change); and Study 7 (threat marginally increased for those imagining a negative future, efficacy increased for those imagining a positive future). Behavioral intentions increased significantly in two studies (Study 1 and Study 4) and decreased in one study (Study 3, White participants only).
More commonly, however, our hypotheses were not supported. There were no significant effects of prospection (positive or negative) in Study 2; we did not increase threat appraisals and behavioral intentions among POC in Studies 3 and 6; we did not increase threat appraisals in Study 4; there were no significant changes in appraisals or behavioral intentions from reading about scientists’ accuracy in Study 5; and there was no change in behavioral intentions as a result of prospection in Study 7.
We also computed simple effect sizes using Cohen’s d by comparing each condition within a study to the control condition(s) in that study (in studies with more than one control condition they were combined together). We then categorized the remaining conditions based on the a priori predictions made before data was collected. We had four types of conditions: those designed to increase efficacy, those designed to increase threat, those designed to increase both efficacy and threat, and those with the potential to decrease threat (in Studies 3 & 6, White participants read that the impacts of climate change would be disproportionately felt by People of Color). The minimum number of participants in a condition was 108; the maximum was 1206. Figure 3 provides a summary of effect sizes within each condition averaged across studies for our three main dependent variables: threat, efficacy, and behavioral intentions. Additional file 1 presents the individual effect sizes for each condition in each study.
Summary of effect sizes across seven studies. Each condition is contrasted to the control condition within each experiment, then effect sizes are averaged across experiments
There is modest support for the malleability of appraisals. The conditions intended to enhance threat showed the largest increases in threat appraisals relative to the control conditions, average d = 0.208. Similarly, the conditions intended to enhance efficacy showed the largest increases in efficacy appraisals relative to the control conditions, average d = 0.209. The effect sizes for behavioral intentions suggest that only those conditions that included an attempt to increase efficacy led to an increase in behavioral intentions (d’s = 0.164 and 0.132 for efficacy and efficacy + threat conditions, respectively). All of these effect sizes are considered small by convention. Additionally, as noted above, within each study these effects often did not reach statistical significance.
Combined data set
Three 5 (Condition: control, efficacy boosting, threat boosting, efficacy & threat boosting, threat lowering) by 2 (climate change belief: Yes vs No) ANCOVAs (controlling for gender and political leaning)Footnote 3 were conducted on threat, efficacy, and behavioral intentions using data combined from all seven studies. Table 6 summarizes the ANCOVA results, and Figs. 4, 5 and 6 show the effects. (The main effect of climate change belief was significant for all three dependent variables, p’s 
Impact of condition and climate change belief on threat appraisals in combined data set
Impact of condition and climate change belief on efficacy appraisals in combined data set
Impact of condition and climate change belief on behavioral intentions in combined data set
For threat appraisals, there was a main effect of condition. The threat boosting condition had significantly higher threat appraisals than the control and threat + efficacy boosting conditions, and marginally higher threat appraisals than the efficacy boosting condition (p = 0.056) and threat reducing (p = 0.052) conditions. Interestingly, the efficacy-boosting condition had lower threat appraisals than all other conditions (p’s ranged from 0.048—0.059).
The 2-way condition by climate change belief interaction (see Fig. 4) was marginal; simple comparisons revealed that the differences in threat appraisals between conditions happened primarily among climate change deniers.
For efficacy appraisals, there was a marginal main effect of condition (see Fig. 5). The efficacy-boosting condition significantly increased efficacy appraisals for both climate change deniers and acknowledgers, p = 0.044, relative to the control condition.
There was no main effect of condition or a condition by climate change belief interaction for behavioral intentions (see Fig. 6).
In sum, messaging designed to increase threat did seem to increase threat appraisals, primarily among climate change deniers. Messaging designed to increase efficacy did increase efficacy appraisals among both climate change deniers and acknowledgers. We found no evidence that messaging impacted behavioral intentions.