This study utilized the survey data from “Knowledge, attitudes, and practices related to COVID-19 in the U.S.,” registered in the Inter-university Consortium for Political and Social Research (ICPSR) . This national survey sought to assess the state of COVID-19-related knowledge, beliefs, mental health, substance use changes, and behaviors among a sample of adults aged 18 years or older currently residing in the United States. The survey was administered online from March 20–30, 2020. Depression and anxiety were assessed using the Patient Health Questionnaire-4, stress was assessed using the Impact of Event Scale-6, and pessimism and changes in tobacco and alcohol use were assessed by the responses to the questionnaire. A total of 6,391 respondents met the eligibility requirements . The study data is a publically avaliable open data set, and all methods were carried out in accordance with the local university’s guidelines and regulations for use of Human data.
To assess the subjective stress of COVID-19, the items of the Impact of Event Scale-6 (IES-6) were adapted (Supplementary Table 1, Additional file 1). The test items consisted of a 4-point Likert scale ranging from 0 to 3 (0 = not at all; 1 = several days; 2 = more than half the days; 3 = nearly every day). The summed score ranged from 0 to 18, with higher scores indicating greater PTSD symptoms.
The IES-6  is a 6-item short version of the Impact of Event Scale-Revised (IES-R)  that measures the principal components of PTSD . The IES-6 demonstrated good sensitivity (r = .88) and specificity (r = .85) with a standard PTSD semi-structured interview conducted by physicians [20,25].
Of the total subjects (n = 6,391), 600 random samples (approximately 10%) were analyzed. Descriptive statistics were used to examine participants’ demographic characteristics. Unidimensionality was examined using principal component analysis (PCA) of Rasch residuals. In addition, once the instrument revealed a single dominant measurement structure, we conducted item-level analysis using the Rasch model, including rating scale analysis, item fit statistics, precision, differential item functioning (DIF), and construct validity. Statistical analyses were performed using SAS v. 9.4 and Rasch analysis was performed using Winsteps v. 4.7.1.
Principle component analysis (PCA) of Rasch residuals
Principal component analysis (PCA) of the residuals was used to examine the unidimensionality assumption in the test items . Unlike conventional factor analysis, PCA of Rasch residuals is performed after excluding the target configuration, and secondary dimensions are detected. Unidimensionality assumes that the eigenvalue for the first contrast is less than 2.0 or that the variance ratio explained by the measurement is greater than 20% .
Local independence means that when the structure level is controlled, the response to the item is not related to another item. To identify local independence, the residual correlation matrix was examined . An average item residual correlation exceeding .20 was interpreted as indicating dependency .
Rating Scale Analysis and Item Fit Statistics
The rating scale model was applied to the six items of the IES-6. To examine the fit of the data to the Rasch model, a rating scale analysis was used. We determined the extent to which the empirically obtained data matched the predictions of the model.
Rating scale analysis criteria. 1) at least ten observations in each rating scale, 2) monotonically advanced average measure in rating scale categories, and 3) outfit mean squares (MnSq) less than 2.0 for rating scale categories .
Item fit. We used the mean square residual (MnSq) and standardized mean square residual (Zstd) to examine item fit. MnSq values between .6 and 1.4 and Zstd values between -2.0 and 2.0 indicate acceptable fit . It is agreed that up to 5% of the sample could demonstrate misfit without being a serious threat to validity . The values provided by this model are expressed in the logit scale, which is a logistic transformation of the observed scores with a mean of 0 and a standard deviation of 1. According to construct theory, suitable items can measure intended unidimensionality and Rasch analysis is a powerful tool for evaluating construct validity . The conditional maximal likelihood estimator (CMLE) was used for the parameter consistency .
Construct validity. The sequence of reasonable or conceptual item difficulties for the assessment item is interpreted as construct validity . In the Rasch model, the difficulty of the evaluation items and the IES-6 score are located in the same linear continuum (logit), and the matching between the evaluation items and the human measurement is presented by the Wright map. We analyzed whether the sequence of difficulty layers of the estimated evaluation items in the Rasch model matched the logical progression from the easiest to the most challenging. Furthermore, we examined whether ceiling and floor effects were at least 5% of the samples in measurements with the maximum and minimum criteria .
Convergent validity. To secure convergent validity, the person measure was correlated with the PHQ-4, which assesses anxiety and depression symptoms. Spearman correlation analysis was used to examine the correlation between PHQ-4 and the IES-6 scores.
Differential Item Functioning (DIF)
In Rasch and item response theory models, the probability of item responses should be a function of the basic characteristic level of people . We conducted a DIF to examine the linear invariant estimation of item difficulty parameters based on the Rasch model . If different group members have the same characteristic level but different response probabilities, the entry represents differential item functioning (DIF). We used the Rasch-Welch t test to compute the size of the DIF . The following are the effect criteria for DIF: (a) a moderate to large DIF (greater than .64 logits in the DIF contrast, thus indicating the difference in item difficulties between the two comparison groups) and (b) a slight to moderate DIF (greater than .43 in the DIF contrast). The significance of DIF contrast was determined at an alpha value of .05 with a two-sided Rasch-Welch t-test .
Personal reliability reflects the degree of impact of measurement scores on measurement errors . In Rasch analysis, every participant is given a Rasch score with an individual person reliability. Personal reliability used the sum score of IES-6 for group comparisons: a score of .7 or higher was considered suitable and .9 or higher was suitable for comparing individual reliability . A person separation index of 2.00 indicates acceptable levels of separation, where a value of 3.00 represents a good separation level. We calculated Cronbach’s alpha to examine the internal consistency of the instrument. A value of .70 is considered acceptable, .80 is good, and .90 is considered excellent .