Construct validity of the self-report instrument of perceived stress in the general Costa Rican population of retirement age

Background It is known that the effects of stress on the body harm health and mortality outcomes. This phenomenon has been widely studied since its conceptualization. Applying self-report instruments to the general population can help identify degrees of stress and provide evidence on how stress affects social relationships, health, and even mortality. This research aims to explore the internal validity of questions of perceived stress in the general Costa Rican population close to pension or retirement age. Methods A nationally representative sample of 2743 individuals born between 1945–1955 in Costa Rica completed a series of questions related to perceived stress. Factor analysis, elements of classical test theory, and a Rasch model were used to generate evidence of scale validity. Results Adequate internal consistency was obtained by factor analysis, with one factor explaining 70% of the variability. The Omega Index value was 0.58. The fit values (INFIT) detected by the Rasch model range between 0.8 and 1.2. Conclusions the items form a scale that refers to the construct of perceived stress and has sufficient internal consistency.


Introduction
The term "stress" in living organisms was de ned by Selye in 1936, building upon the knowledge of the time that Bernard and Cannon had already de ned about the milieu intérieur, which referred to the balance of the internal environment through the homeostasis of the interstitial uid. (1). Selye conceived the organism as a dynamic system seeking to maintain that internal equilibrium, known as homeostasis (2). He de ned stress as "a non-speci c response of the body to any demand for change" (3)(4)(5)(6). Page

Participants
The Costa Rica Longevity and Healthy Aging Study (CRELES) is a set of longitudinal, nationally representative surveys of the health and life experiences of older adults in Costa Rica. CRELES is part of a growing set of health and retirement surveys being conducted around the world, including studies led in the United States (Palloni et al., 2013), (33), Mexico (34), and other Latin American countries (

Stress Measurement Tools
Perceived stress was measured by the following series of questions: -Problems at your job, do they make you feel stressed or anxious? -Family relationships, do they make you feel stressed or anxious?
-Your health, does it make you feel stressed or anxious? -Your nancial situation, does it make you feel stressed or anxious?
-Parents or other family members' health, does it make you feel stressed or anxious?
-Perceived stress about helping to care for a family member.
When individuals answered positively to any of these questions, they were asked how long they had been feeling stressed, with response options of more than a year or less than a year. Furthermore, they were asked about the perceived stress of helping a family member with basic activities such as dressing, eating, or bathing due to a health problem. If individuals were not assisting any family member in this regard, it was considered as having no stress caused by this aspect.
In the case of individuals who did not perform paid work outside the home, it was considered as having no work-related stress. Most of these cases involved women (n = 1269). Likewise, 13 individuals reported having no family, and therefore, it was assumed they experience no stress related to family relationships or parents' health.
Data from 2743 individuals were analyzed, for including only the cases where all items of the scale were fully completed. If an individual required another person (proxy) to answer the interview, stress-related questions were not asked, and those cases were excluded from this analysis.

Data Analysis
The rst step was to validate whether the six questions were aligned in the same direction to form a scale. This is known as the unidimensionality of the questions. The factor analysis of principal components (FAPC) was applied, using a tetrachoric correlation matrix (38). Factor analysis is a multivariate technique commonly used in elds such as psychology or other behavioral and health disciplines. It is employed when measuring certain concepts directly results challenging, as in this case, stress.
The current practice is to measure concepts indirectly by collecting information on related aspects that can be directly measured or observed. These related aspects are aggregated into a single construct, known as the "latent variable", which is assumed to be an indicator of the concept being measured. Hence, factor analysis helps establish the relationship between the latent variable (not directly measured) and the observed variables (approximated).
The underlying model of the method is essentially multiple linear regression where the focus of interest is on explaining the covariance or correlation structure (or both), This helps determine whether the p response variables exhibit patterns of relationship among themselves, allowing them to be de ned in m subsets of closely related variables that differ from the variables in other subsets.
In addition, Cronbach's alpha (39) and Omega (40) coe cients were calculated as reliability coe cients. A maximum value of 1 of Cronbach's alpha coe cient indicates a maximum level of reliability (39,41), meaning the observed responses are reproducible. Factor analysis and calculation of coe cients were performed using Stata.
Another evaluated aspect was the presence of items that are either di cult to answer or do not contribute effectively to the measurement of perceived stress. A Rasch analysis was used for this purpose. According to Prieto and Delgado (42), Rasch analysis is based on a mathematical model that describes the relationship between the probability of a correct (or prede ned) response to an item and the difference between the ability of the respondent. The procedure assesses the t of each response and item to a unidimensional model, where a single construct or latent variable underlies and is re ected in the correct response to the item (43). The Rasch model analysis was performed in the Winsteps package, version 3.80.1. Table 1 shows the main sociodemographic characteristics of the participants. The study included a total of 1674 women and 1069 men, 5% of whom were living in the blue zone of Nicoya. The average age was 59 years for both groups. Among women, 59% reported being married or in a consensual union, while this percentage rose to 83% among men. Furthermore, nearly 6 out of 10 participants indicated having completed only elementary or basic education high school, with 58% of women and 56% of men falling into this category. The highest prevalence of stress was attributed to one's health, nancial situation, and parental health. Moreover, there were statistically signi cant differences in the reporting of stress causes between men and women. For instance, 36% of men and 50% of women reported stress related to their health. This pattern of higher prevalence among women was consistent for all other stress causes, except for workrelated stress, explained by the fact that many women in the sample do not perform paid work outside the home (n = 1269). Additionally, the analysis indicated that the perception of caregiving stress was not widespread, which can be explained by the relatively low percentage of caregivers in the sample, accounting for 11.4% (11.4%) (Fig. 1).

Unidimensionality
The tetrachoric correlations between the items show a medium-intensity relationship between them, as the correlations are of the order of 0.20 or higher between most items. The item related to caregiving displayed the lowest correlation with all the other items. However, the correlations with this item were in line with expectations. There was a very low and negative correlation (-0.069) between the item measuring work stress and caregiving, suggesting that individuals experiencing work stress were less likely to engage in caregiving tasks. The highest correlation of the caregiving stress item can be observed between the caregiving stress item and the item assessing stress related to the health of parents or other close relatives (0.357) ( Table 2). An exploratory factor analysis (by principal components) was performed, using this structure of tetrachoric correlations and the result revealed the presence of a single dimension. This factor explains 70.12% of the total variance. The Kaiser-Meyer-Olkin test yielded a value of 0.71, suggesting that data t the factor analysis and supporting the hypothesis that data are correlated and that, in this case, a single coherent or latent factor can be identi ed (Table 3).

Reliability
Based on the results of the factor analysis con rming the unidimensionality of the questions, a reliability analysis was conducted using classical test theory indicators, including the Alpha and Omega coe cients, as well as a Rasch model. Table 4 shows the statistics of the items under study. Very few individuals are involved in caregiving (n = 305), hence only 5% of respondents reported feeling stress from caring for sick people. Indicators, such as Cronbach's alpha and the Omega coe cient, measure the internal consistency of the items which, in general terms, is an evaluation of how reliably they measure the construct they are intended to approximate. In this study, these indicators yielded values of 0.553 and 0.5415, respectively.

Rasch Model
The Rasch model allows solving some of the de ciencies of the Classical Test Theory, particularly, joint measurement, by expressing parameters of individuals and items in the same units. It also allows the quanti cation of the t of the response patterns to the model, as responses to the items solely depend on the individual's skill levels, or in this case, on the perception of stress.
The reliability index for both individuals and items was calculated using a Rasch model. In the case of individuals, this measure indicates how consistent the results are if another subset of items from the same construct were applied to the same group of individuals. Here, the reliability indicator for individuals yielded a value of 0.35.
On the other hand, the reliability of the items indicates the consistency of the estimates of the di culty parameter if the same set of items is applied to another group of individuals with similar characteristics. In this case, the estimated value was 1.00, indicating that the Rasch estimates are highly consistent. This result can be attributed to the large sample size. It's worth noting that while this indicator is similar to Cronbach's alpha in the Classical Theory approach, they are not comparable.
The main objective of the Rasch model is to identify two aspects: 1) people who answer the items positively because they really are under conditions that generate stress and 2) properly formulated items that are only answered positively by people who really feel stress. This is referred to as model t.
To assess individuals' t to the model, di culty measures and t statistics (INFIT MNSQ) were employed. According to the measure indicator, the item "Relatives health" was found to be the easiest, with a higher proportion of individuals reporting stress related to the health of their parents or family members compared to other items. Conversely, "Take care of sick relatives" was the most di cult item, as only a few individuals reported feeling stressed about this activity. The INFIT values for all six items fell within the acceptable range of 0.8 to 1.2, indicating adequate t (Table 6) (42).   In this case, although the map adequately depicts the distribution, it is evident that additional items need to be added to the instrument, to ensure that they measure the same construct. It is once again apparent that the most challenging item to respond positively to is the one related to the stress of caring for sick relatives, aligning with the earlier observation that very few individuals engage in this activity and experience stress as a result.
Furthermore, if the model is rerun with the exclusion of the item "Take care of sick relatives," the indicators remain satisfactory, with INFIT values of the remaining ve items still falling within the acceptable range of 0.8 to 1.2. The reliability of person is 0.32.

Discussion
This study reveals that stress is most reported concerning personal health, nancial circumstances, and the health of parents and relatives.
Furthermore, it was found that there are signi cant differences in the perception of stress between men and women, with women reporting higher levels of stress.
In terms of the measurement of perceived stress using the items employed in this study, the Classical Test Theory (TCT) analysis indicates that the scale demonstrates good internal consistency. The factor analysis supports the unidimensionality of the construct, with all items loading onto a single dimension and explaining a substantial proportion (70%) of the variability in the data. The reliability coe cients, such as Cronbach's alpha and Omega, were found to be 0.5714 and 0.5777, respectively, when considering binary response data.
The result of the application of the Rasch model demonstrates an adequate overall t of the items to the model. However, it was observed that the item "Take care of sick relatives" does not t the model and does not correlate with the other items. This lack of t can be attributed to the low number of individuals who are caregivers and experience stress in this speci c context. According to Rasch's model, after removing this item, the remaining items in the scale t well into the stress measurement model. (42). Moreover, it is worth noting that the item related to stress about the health of parents or relatives shows some lack of t, albeit to a lesser extent and in the opposite direction, as it re ects the highest prevalence of stress. In conclusion, the items included in the scale exhibit su cient internal consistency and collectively represent the construct of perceived stress.
The items utilized in this research are also applied in the Taiwan Longitudinal Study on Aging (TLSA). (44). Both the Taiwan and Costa Rica studies are part of the growing set of health and retirement surveys being carried out in other latitudes, such as the United States. (33), Mexico (34) and other Latin American countries (35)(36)(37). These studies were designed to be comparable with each other and do not use speci c scales to measure stress such as the Stress Appraisal Measure (SAM). (45), Impact of Event Scale (IES) (46) or the Perceived Stress Scale (PSS) (47). Cronbach's alpha observed for Costa Rica is lower than that observed in Taiwan. Although these are low reliability values, the factors can be attributed to the small number of items included and to the fact that, unlike Taiwan, the measurement in Costa Rica was done based on a binary scale (yes-no).
There have been no population studies in Taiwan that have reported using the Rasch analysis. For its part, this study offers a broader perspective as it further explores the construct validity and dimensionality of the stress measurement questions by applying a modern theory within the framework of parametric analysis, as Rasch models do.
The use of the Rasch model in this study is a signi cant strength as it overcomes the limitations of the Classical Test Theory. Additionally, the study bene ts from a large sample size and the random selection of a general population, rather than focusing solely on hospitalized individuals. However, it is important to acknowledge that the items used in this study have a disadvantage related to their wording. They may appear to be asking about two situations or emotions simultaneously when assessing whether the situation causes stress or anxiety.
Perceived stress is commonly described in the literature as the extent to which an individual assesses their life as stressful. It encompasses emotions such as feeling stressed, upset, or angry, as well as cognitive evaluations that one lacks control or that the demands of a situation outweigh the available coping resources (48). On the other hand, anxiety is described as an anticipated emotional response to perceived danger or threat, which can occur independently of speci c stressors (49,50) and is often associated with uncertainty about the future. Therefore, it is recommended that future research treat these concepts separately and explore them individually.
Based on the psychometric indicators, the items used in this study do form a scale for measuring perceived stress. However, it is recommended to expand the scale by including a greater number of items that clearly measure the same construct. This would help improve the statistical properties of the scale and provide a more robust instrument for research purposes and the development of policies aimed at enhancing health and quality of life.
For future studies, it is suggested to compare the scale used in this study with established stress measurement scales such as the Perceived Stress Scale (PSS). It is also recommended to complement the scale with an objective measurement such as cortisol to serve as a gold standard for validating the items presented in this study. This could also lead to the development of new items that provide a more accurate assessment of perceived stress.
In addition, to ensure an understanding of the items and the measurement of the construct, it is advisable to conduct qualitative interviews as a complementary approach. Furthermore, it would be desirable for the questions to be applicable to all populations, including individuals who do not work outside the home.
In conclusion, the questions used in this study are appropriate for measuring stress. The ndings provide statistical evidence for a unidimensional scale, as supported by factor analysis and the Rasch model, which is a recognized standard for modern psychometric assessments of outcome scales. However, one item pertaining to the care of sick individuals is not suitable for measuring general stress due to the low prevalence of caregivers in the sample. To enhance the scale's reliability and validity, it is recommended to expand the number of items, ensuring they measure the same construct of perceived stress. Additionally, comparing the results with an objective measurement such as cortisol can provide further validation and a more comprehensive understanding of stress levels.

Declarations
Ethics approval and consent to participate.
CRELES project studies were reviewed and approved by The Scienti c Ethics Committee of the University of Costa Rica (references: VI-2878-2009, VI-5308-2009, and VI-1313-2012). The study of the retirement cohort was also approved by the Committee for Protection of Human Subjects (CPHS II) at the University of California, Berkeley. The participants provided their written informed consent to participate in this study, and all methods were performed in accordance with relevant guidelines and regulations.

Consent for publication
Not applicable Availability of data and materials The datasets presented in this study can be found in online repositories at: http://www.creles.berkeley.edu/

Competing interests
The author declares no competing interests.

Not applicable
Authors' contributions EMC contributed to conception and design of the study, organized the database, performed the statistical analysis, and wrote the manuscript.