Pessimism

We developed a questionnaire that initially included 79 items assessing each of the domains through their related key constructs (see Additional file
1). Constructs within domains were selected based on conceptual relatedness to the content of the domain (i.e., Knowledge, Procedural knowledge, Skills, Professional role, and Memory); inclusion in relevant theories frequently used in the field of behavior change (and thus ready access to existing items): the Theory of Planned Behavior
[41 (link)] (i.e., Perceived behavioral control, Attitudes, Subjective norm, and Intention) and Social Cognitive Theory
[42 (link)] (i.e., Self-efficacy, Outcome expectancies, and Social support); existence of validated scales (i.e., Optimism, Pessimism, Action planning, Attention, Affect, Stress, Automaticity, and Self-monitoring); and/or relevance to the implementation of PA interventions in routine healthcare by mapping factors resulting from previous research
[43 (link),44 (link)] onto the TDF domains. JP and JMH independently identified that the constructs Reinforcement, Priority, Resources/materials, and Descriptive norm were salient in the previous PA-based research and thus these constructs were also included as construct-indicators of their respective domains.
Items measuring constructs within the domains Knowledge, Beliefs about capabilities, Optimism, Beliefs about consequences, Intentions, Social influences, Emotion, and Behavioral regulation were adapted from previously published questionnaires (i.e.,
[34 (link),35 (link),41 (link),42 (link),45 -53 ]). Given lack of available questionnaires in the literature for some domains, new items were created for the domains Skills, Social/professional role and identity, Reinforcement, and Environmental context and resources. With regard to the domain Goals, items were newly developed for the construct Priority (as none could be located in the literature), while items measuring the construct Action planning were adapted from a previously published questionnaire
[46 (link)]. With regard to the domain Memory, attention, and decision making, items measuring the construct Attention were adapted from a previously published questionnaire
[51 (link)] and items measuring the construct Memory were newly developed. New items were developed based on discussions between JP and JMH. These discussions were informed by the academic literature on the concept and definition of specific domains and constructs, questions to identify behavior change processes as formulated by Michie et al.[31 (link)], and themes emerging from interviews on the implementation of PA interventions
[43 (link)]. WAG and MRC supervised the development of the questionnaire and reviewed items’ face validity.
To develop a questionnaire which could be used by researchers in different fields of implementation research, items were formulated in a generic way using a '[action] in [context, time] with [target]’ construction based on the 'TACT principle’
[38 ], whereby researchers can specify the target, action, context, and time relevant to their research. The questionnaire was developed in English, then translated to Dutch and back-translated to English by an independent translator. The small amount of differences between the original and back-translated version of the questionnaire were discussed and adaptations were made.

For each simulation, we calculated the following measures for goodness-of-fit:
R², using the most general definition [5 (link),8 (link)]:
Formula 10:
with RSS = residual sum-of-squares, TSS = total sum-of-squares, y = response values, = fitted values and = the mean of response values. For a more detailed description see Remarks 1-6 in Additional File 1.
We chose to use the adjusted R² to compensate for possible bias due to different number of parameters:
Formula 11:
with n = sample size and p = number of parameters.
The Akaike Information Criterion (AIC, [10 -12 (link)]), a measure that is widely accepted for measuring the validity within a cohort of nonlinear models and frequently used for model selection [13 ].
Formula 12:
with p = number of parameters and ln(L) = maximum log-likelihood of the estimated model. The latter, in the case of a nonlinear fit with normally distributed errors [13 ], is calculated by
Formula 13:
with x₁, ..., x_n = the residuals from the nonlinear least-squares fit and N = their number.
To provide a fair playing ground, we employed an AIC variant that corrects for small sample sizes, the bias-corrected AIC (AICc):
Formula 14:
with n = sample size and p = number of parameters.
In order to obtain values for the validity of a fit, we used Akaike weights which calculate the weight of evidence for each model within a cohort of models in question [12 (link)-14 ]:
Formula 15:
with i, k = model numbers, Δ_i(AIC) = the difference in AIC of each model in comparison to the model with the lowest AIC, subsequently normalized to their sum (denominator).
Also here, we used the bias-corrected AICc for calculating the Akaike weights.
We also chose to employ the Bayesian Information Criterion (BIC), which gives a higher penalty on the number of parameters [15 (link)]:
Formula 16:
with p = number of parameters, n = sample size and L = maximum likelihood of the estimated model.
Furthermore, the residual variance as the part of the variance that cannot be accounted for by the model:
Formula 17:
with RSS = residual sum-of-squares, n = sample size and p = number of parameters.
The variance of a least-squares fit is also characterized by the chi-square statistic defined as Formula 18:
where y_i = response values, f(x_i) = the fitted values and = the uncertainty in the individual measurements y_i. We further define the reduced chi-square as a useful measure [16 ] by
Formula 19:
with ν = n - p (degrees of freedom). If the fitting function is a good approximation to the parent function, then the variances of both should agree well, and the reduced chi-square should be approximately unity. If the reduced chi-square is much larger than 1 (i.e. 10 or 100), it means that one is either overly optimistic about the measurement errors or that one selected an inappropriate fitting function. If reduced chi-square is too small (i.e. 0.1 or 0.01) it may mean that one has been too pessimistic about measurement errors. For this work, models were selected based on reduced chi-square by being closest to 1.

No sample size calculation was done due to the exploratory nature. For the primary outcome, we performed an estimate of the precision. Given a precision of ± 3% and assumed proportion of 30% self-sampling (enrolled subjects), a sample size of 1200 WLWH estimates a 95% confidence interval completely within the required precision. In the pessimistic case with a given a precision of ± 2% and assumed proportion of only 10% self-sampling (enrolled subjects), a sample size of 1200 WLWH estimates a 95% confidence interval completely within the required precision.

During the pandemic, a self-made scale was used to measure residents' uncertainty. The scale contains six questions (Table 2) that asks subjects about their perceptions of the spread of the pandemic and their own infection, as well as their perceptions of the future development of the pandemic. The Likert scale with 5 points was adopted for all questions (from 1 strongly disagreed to 5 strongly agreed). The higher the subjects' average score, the higher their perception of the risk of pandemic spread and infection, and the higher their pessimistic perception of the future development of the pandemic. In this study, the Cronbach's α score for this scale was 0.93.
The scores of uncertainty ranged from 1 to 5, and 3 points indicated that the uncertainty of the subjects was in the middle level. According to the distribution of subjects' uncertainty scores (Figure 1), we divided them into two groups: the medium-high group (with scores ≥3) and the low group (with scores <3). Finally, we obtained that there were 209 subjects in the medium-high group and 311 subjects in the low group, and there were significant differences in the scores of uncertainty between such two groups [t₍₅₂₈₎ = 29.93, p < 0.001].

People's inherent psychological traits can have an impact on positive life attitudes, depression levels, and pandemic preventive behavior intentions. Personality, as the sum of an individual emotions, thoughts, and behavioral tendencies, plays an important role in this process. Previous studies have shown that people's mental health (33 (link)), positive life attitudes (34 (link)) and behavioral tendencies (35 (link)) are significantly influenced by personality. For example, individuals with higher neuroticism scores were more likely to be depressed and have a pessimistic outlook on life (36 (link), 37 (link)). Individuals with higher conscientiousness scores were more likely to adopt preventive behaviors during the pandemic (38 (link), 39 (link)). To exclude the interference of personality on the findings, we included personality as control variables in this study. The Big Five personality scale developed by (40 (link)) was used in this study to measure the personality of the subjects. The scale contains five dimensions: neuroticism, conscientiousness, agreeableness, extraversion, and openness, and each dimension contains eight questions. The Likert scale with 5 points was adopted for all questions (from 1 very disagreed to 5 very agreed). In this study, the Cronbach's α scores were 0.91, 0.85, 0.71, 0.94, and 0.79, respectively.