Development of a social and professional stress scale for parents of children with autism spectrum disorder 1

Parents of children with Autism Spectrum Disorder (ASD) may experience increased stress in their social and professional activities due to the challenges of raising a child with ASD. The present study developed a scale to measure the Social and Professional Stress (SPS) experienced daily by these parents. The study sample consisted of 255 parents residing in Brazil aged between 21 and 61 years (mean = 38, SD = 6.0). Item Response Theory (IRT) was used to develop the SPS-Scale, which showed good psychometric properties. Our findings indicated a higher level of SPS among mothers who are primary caregivers and who have children with symptoms of ASD at medium or severe levels. The child's age and the interviewee's marital status also showed an association with the SPS experienced by the parents. Overall, the SPS-Scale proved to be a valid instrument to measure the SPS experienced daily by parents of children or adolescents diagnosed with ASD.


Introduction
Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder characterized by difficulties in communication and social interaction, restricted interests, and stereotyped behavior patterns (American Psychiatric Association, 2013).Diagnosing ASD can be difficult because there is no specific medical test to diagnose this disorder.Parents often notice the child's atypical behavior, which helps doctors make the diagnosis.Although there are several studies on ASD, its causes are still unknown (Teixeira, 2016).Three levels of autism are indicated based on necessary support levels: level 1 (requiring support) is the mildest, while level 2 (requiring substantial support) and level 3 (requiring very substantial support) are the middle and most severe, respectively.
The great attention and high daily demand for care required by children with ASD often cause physical, financial, social, and emotional stress for their parents (Al-Oran & AL-Sagarat, 2016; Aguiar & Pondé, 2018).Mothers are generally the most affected (Kiami & Goodgold, 2017), as they usually assume the role of primary caregivers.Some common stressors are the child's behavior, difficulties with the work schedule, a great concern with the child's school stage, difficulties with the child's daily care demands, and uncertainty about the child's future (Miranda et al., 2019).
To avoid exposing the child with ASD and their difficulties in participating and interacting in social activities and events, parents often feel forced to stay at home because of the challenges they experience with the child's behavior (McStay et al., 2014).Some parents also face prejudice in their social networks because of the child's behavior and often report changes in their social relationships with family and friends, making social interaction increasingly restricted (Whitman, 2015).
On the other hand, some parents of children with ASD are forced to leave the workforce (most often mothers) because they cannot obtain appropriate childcare or a flexible work schedule (Minatel & Matsukura, 2014).Those who remain at work are concerned with the workload that interferes with the time to practice activities that influence the child's development.Furthermore, employment decisions are often related to financial issues, which can also be a source of stress (Veld et al., 2017).The study by Ou et al. (2015) conducted in China with 459 nuclear families of children with ASD revealed that childcare problems greatly affected employment decisions of 57.5% of them.
The family's ability to adapt to the child's needs is also essential, as it can directly interfere with how the child with ASD will develop their skills (Miele & Amato, 2016).Therefore, offering support and professional help to parents of children with ASD and their family members is crucial to help them adapt to changes and deal with the child's care demands (Aguiar & Pondé, 2018).
Psychometric scales are valuable tools that can help assess ASD traits and their effects on parents' lives.Using objective instruments (questionnaires) for psychometric assessment, methods based on Item Response Theory (IRT) allow the construction of scales to measure latent traits (Sartes & Formigoni, 2013), i.e., traits that cannot be measured directly (such as attitudes, quality of life, patient satisfaction, amongst other attributes).IRT models can evaluate the relationships between the latent trait of interest and the items intended to measure the trait.For instance, the graded response model (Samejima, 1969) is appropriate when items have ordered response categories on a rating scale.
Several studies have shown the importance of IRT for psychometric assessment.For example, Sturm et al. (2017) used it to investigate the Social Responsibility Scale (SRS) psychometric properties and produce a reduced 16-item SRS short form that emerged as a more precise measure of ASD core symptom severity.Gardiner et al. (2019) also used methods based on IRT to assess the psychometric properties of the Family Resilience Assessment Scale, composed of 6 subscales that identify protective factors for parents of children or adolescents with ASD.
In addition, IRT methods were used by Zaitman-Zait et al. (2010) to assess the functioning of items in the Parenting Stress Index-Short Form (PSI-SF) to measure the stress of parents of young children with ASD.PSI-SF is a derivative of the PSI (Abidin, 1995) developed to measure parents' stress of typically developing children.It includes 36 items in three subscales (parental distress, parent-child dysfunctional interaction, and difficult child), each containing 12 items.The authors concluded that nine items showed poor functioning among parents of children with ASD.The reason is that children with ASD behave differently from typically developing children, and these items may not adequately discriminate the stress severity of parents of children with ASD.Two other studies that used the PSI-SF with parents of children with ASD also concluded that some items related to parent-child interaction and child's behavior could be perceived differently by parents of children with ASD and those of typically developing children (Zaitman-Zait et al., 2011;Dardas & Ahmad, 2014).Thus, the proposal of new instruments with items explicitly aimed at parents of children with ASD seems justifiable.
Social and Professional Stress (SPS) experienced by parents of children with ASD is a latent trait difficult to measure and not widely covered by existing scales.Thus, this study aimed to (1) propose an instrument to measure the SPS experienced by parents of children with ASD; and (2) investigate parental and child characteristics predicting higher levels of SPS.It is noteworthy that the instrument proposed in this study does not include challenges such as parents' fears about the child's future, as the focus is on social and professional (work) situations they experience due to the child's ASD condition.
The instrument's items related to professional situations (P1 to P7, Table 1) ask about the influence of the child's ASD condition on the parents' professional life (e.g., in their work routine).In contrast, items related to social situations (S1 to S7, Table 1) ask about this influence on the parents' social life (e.g., social relationships and participation in parties and social events).The Portuguese version of the items is in Appendix A (Table A.1). Items having three or more ordered response categories were scored following a Likert scale (Likert, 1932), as shown in Table 1.The lowest and highest scores were assigned to the categories believed to cause the lowest and highest level of parental stress, respectively.A group of specialists (psychologists, linguists, and statisticians) and some invited parents of children with ASD evaluated the first version of the instrument, aiming to test its format and function, clarity of the message, and language adequacy.The convenience and intentional sample of the pilot test consisted of 10 participants (seven women and three men), with a mean age of 39.The suggestions were incorporated after the pilot test, and none of the items needed to be excluded.

Participants and Recruitment Procedure
Participants were recruited through social networking sites, including Facebook, WhatsApp, Instagram, and Twitter.The questionnaire was edited into a Google Form®, and its web link remained available from February 1st to April 31st, 2020.Participants eligible for participation were parents of children or adolescents with ASD residing in Brazil aged 18 years or older.Participation was voluntary, and all participants who met the inclusion criteria and agreed to participate provided electronic informed consent.All parents with paid employment at the time of the survey completed all items (Table 1); otherwise, they completed items S1 to S7.
Participants were also asked about themselves and their children (see questions in Table A.

of Appendix A
).Two open-ended questions also allowed them to comment on the impact of the child's ASD condition on their professional and social lives.The data considered in the analysis were those of parents with paid employment at the time of the survey.The Research Ethics Committee of the Federal University of Parana, Brazil, approved the study (Protocol No. 3743074).

Analysis of the IRT Assumptions
IRT methods assume that individuals vary along a dominant latent continuum.The necessary premises for unidimensional IRT models are unidimensionality, local independence, monotonicity, and item invariance.Since unidimensionality implies that only one latent trait is measured by the set of items in the instrument, factor analyses of the polychoric correlation matrices were first conducted to examine the essential unidimensionality.Scree plots of the eigenvalues of factors and principal components analyses were used to determine the number of factors or principal components to retain.Gorsuch (1983) recommends a ratio of the first to second eigenvalues equal to or greater than 3 to indicate essential unidimensionality.These analyses were carried out using the 14 items in Table 1.Several psychometric indices discussed by Rodriguez et al. (2016) were also evaluated.They are the omega reliability coefficients (omega and omega H), explained common variance (ECV), factor determinacy (FD), and construct replicability (H).
Local independence was evaluated using the local dependence (LD) G 2 statistic presented by Chen and Thissen (1997).Furthermore, the discrimination parameter of the Graded Response Model (which represents a slope) was also examined to assess possible violations of local independence.Items displaying excess dependence may have very high slopes (e.g., greater than 4) relative to other items on the measure (Nguyen et al., 2014).Item trace plots showing the items' characteristic curves (ICC) or items' operation characteristic curves (OCC) helped examine the monotonicity (i.e., that the probability of endorsing an item will continuously increase at higher levels of the latent variable).
Finally, the estimated item parameters were compared across different groups (e.g., gender and age groups) to test for item invariance.If the model fits, the anchor items must show no differential item functioning (DIF) in the parameters between different groups.In other words, item calibrations using different groups should yield similar parameter estimates (Nguyen et al., 2014; Fidalgo & Quintanilla Cobian, 2018).

Item Analyses Based on the Graded Response Model
Item analyses based on IRT parametric models are normative tests of item performance, providing a way to measure the quality of items.This study used the unidimensional Graded Response Model (GRM) by Samejima (1969) to calibrate the items' parameters and select items with good performance.Under this model, the probability of an individual j with latent trait   (j = 1, ..., n) endorsing the category equal to or higher than  from the i-th item is given as for  = 0, 1, ..., ci -1, where ci is the number of categories of the i-th item.Given that  ,0 + (  ) = 1, the parameter for the lowest category  ,0 is not estimated.The probability of endorsing the category  is computed by subtracting the adjacent probabilities such that The discrimination parameter  represents a slope, which refers to how well the item response options discriminate (or differentiate) between parents with high and low levels of SPS.An item provides ample information about SPS differences across individuals if its discrimination is high.Otherwise, the item does not provide much information and may indicate that it needs to be adjusted or removed.The difficulty parameter  indicates where the item falls on the continuum of the latent trait.The parameters  , (i.e., threshold values) are interpreted as how high an individual's SPS level needs to be in order to have a 0.5 probability of endorsing that given response category or a higher category.In the present study, the selected items were those satisfying: 0.8 ≤   < 4.0 and -3 <  , < 3, with  ,1 ≤  ,2 ≤ ⋯ ≤  (  −1) .Response categories with a rate close to zero were regrouped to calibrate better the item's parameters (Sartes & Formigoni, 2013).
After estimating the GRM parameters using the maximum likelihood approach, the expectation a posteriori method was used to estimate the latent trait θ, assumed normally distributed with mean zero and unit variance (Embretson & Reise, 2000;Baker & Kim, 2004).

SPS-Scale Construction and its Interpretation
The SPS-Scale was constructed based on positioning the anchor or quasi-anchor items that characterize each scale point.Since the latent trait θ was assumed to be normally distributed with mean zero and unit variance, the items with the greatest discrimination were fixed on each scale unit, basically in the range of -3 to +3, with  −1 <   two consecutive levels of the scale.For category  of an item to be positioned at a certain level   of the scale, three conditions must be satisfied simultaneously: (1) the category  has a probability ≥ 0.6 of being endorsed by parents with  ≥   ; (2) the category ( − 1) has a probability < 0.5 of being endorsed by parents with  ≥  −1 ; and (3) the difference of the probabilities associated with categories  and ( − 1) is ≥ 0.3.
Items that simultaneously meet all three conditions are called anchor items.As it is difficult to fulfill all of these conditions, items that met two conditions, called quasi-anchors, were considered (Barbetta et al., 2014).After positioning the anchor and quasi-anchor items on the SPS-Scale, the scale levels were defined and interpreted.

Description of Participants
The sample consisted of 255 parents, 222 mothers and 33 fathers aged 21 to 61 years (mean = 38, SD = 6.0).Overall, 78.4% were married, 91% were the primary caregivers, and 56.5% received support from their family or close people to help them with the child's daily care demands.The age of children or adolescents (217 males and 38 females) ranged from 1 to 18 years (mean = 6.5, SD = 3.7).Their age at ASD diagnosis ranged from 1 to 15 years (mean = 3.5, SD = 2.6).

Dimensionality Analysis
The Scree plot (Figure 1) suggests that one factor or principal component is sufficient to retain, with the ratio of the first to second eigenvalues ≥ 3 indicating essential unidimensionality.The omega reliability coefficients (omega = 0.89, omega H = 0.71) indicate that the general factor is the dominant source of systematic variance.The ECV of 0.58 also evidenced that the common variance is essentially unidimensional.In addition, high factor determinacy and construct replicability for the general factor (FD = 0.93, H = 0.89) suggest a well-defined latent variable.Then, the unidimensional GRM was considered for item parameter estimation and item analysis.PC: principal components and FA: factor analysis.

IRT Parameters Estimation Based on the GRM
The IRT parameter estimates for item discrimination and item difficulty in Table 2 show that all items on the SPS instrument performed well (0.8 ≤   < 4.0 and -3 <  , < 3).The difficulty parameters (threshold values) are on the same scale as the Z-scale, where a normal distribution is centered at zero with a unit standard deviation.
For example, item S3 has the following threshold values: b1 = −0.76,b2 = 0.44, and b3 = 1.5.These values are the cutoff points that intercept the lines representing the probability of endorsing a category given a certain level on the latent trait represented by the x-axis in the trace plot shown for item S3 in Graph (a) of Figure 2. Thus, parents with an SPS level below the first threshold (-0.76) have a high probability of endorsing the category  = 0 (never or rarely) of item S3.In addition, parents with an SPS level between −0.76 and 0.44 are most likely to endorse the category  = 1 (sometimes), whereas those with an SPS level between 0.44 and 1.5 are most likely to endorse the category  = 2 (often).
Finally, those with an SPS level above 1.5 are most likely to endorse the category  = 3 (very often).
Graph (b) in Figure 2 shows the monotonicity of item S3 since the curves do not cross and continually increase at higher levels of the latent variable.The trace plots for all items are displayed in Figure 3.They show the item-level information regarding the performance linked to each response category.Items with larger discrimination levels tend to provide information about the parents' SPS in a narrow range (e.g., item S6, which had the largest discrimination value of 2.65).The test information curve shown in the last plot in Figure 3 indicates that the SPS instrument is best suited for measuring the SPS level in the range from -2 to 2 (where the curve is highest).Then, the SPS instrument provides more information (or assesses more accurately) parents with SPS in this range.

Item Fit and Local Dependence
After controlling for the false discovery rate (FDR), a correction of multiple comparisons that is better suited in IRT models than the Bonferroni correction (Depaoli et al., 2018), the S-X 2 item fit statistic evidenced that the items fit the questionnaire well.There were also no issues with LD, as the local independence assumption among items on the SPS-Scale was supported by the LD G 2 test (pvalues > 0.05), as well as by discrimination parameters smaller than 4.0 (Table 2).
Results (not shown) supported item invariance across age groups (≤ 38 and >38 years), indicating that parents of children with ASD of different ages similarly interpreted all items.Item invariance across gender could not be assessed because of the small number of fathers in the present study.

SPS-Scale Levels and Interpretation
The items identified as anchor items were: S1, S3, S4, S6, and S7, and as quasi-anchor: P1 to P7, S2, and S5.After positioning the items that characterize each scale point, five levels were defined for the SPS-Scale.These levels and their interpretations are shown in Table 3.
The scale levels in terms of the overall SPS score (OS) are also shown in Table 3.This score, computed by adding the responses of all 14 items in Table 1, ranges from 14 to 55.The higher the score, the higher the SPS level.In this study, latent trait estimates and overall SPS scores showed a correlation of 0.96 (95% confidence interval: 0.95 to 0.97).
Based on the five levels defined for the SPS-Scale (Table 3) and the estimated values of θ, 42 parents (16.5%) in the present study were classified as having a very low SPS level and 77 (30.2%) as having a low SPS level.For the moderate, high, and very high SPS levels, the number of parents classified on them was 101 (39.6%), 29 (11.4%), and 6 (2.3%), respectively.At this level, there is a very low SPS.Parents of children with ASD are highly likely to endorse that their child's ASD condition has little or no impact on their professional life, and the same goes for their social life. Low At this level, there is a low SPS.Parents of children with ASD are highly likely to endorse that: (a) sometimes have difficulties with their work routine because they have no one to leave their child when they need to; (b) the child's daily care demands sometimes affect their work routine (e.g., missing work); (c) when attending parties or events with the child, they can have a little fun and interact a little with people; (d) the child's ASD condition interferes a little in their social life, and (e) the child's daily care demands have some impact on their social life. Moderate At this level, there is a moderate SPS.Parents of children with ASD are highly likely to endorse that: (a) the child's daily care demands make them tired, which often interferes with their work activities; (b) they have been able to dedicate little or nothing to their professional life since the child's ASD diagnosis; (c) the change in their workload due to the child's daily care demands was unfavorable to them; (d) they prefer to stay at home to avoid places that interfere with their child's behavior; (e) sometimes they avoid going to certain places due to their child's behavior and comments aimed at their child, and (f) rarely or sometimes they are not invited to parties or social events due to their child's behavior. High At this level, there is a high SPS.Parents of children with ASD are highly likely to endorse that: (a) they often have difficulties with their work routine because they have no one to leave their child when they need to; (b) the child's daily care demands make them tired, which very often interferes with the performance of their work activities; (c) the child's daily care demands often affects their work routine (e.g., missing work); (d) the child's condition interferes too much in their professional life; (e) it is difficult reconciling their work routine with the child's daily care demands; (f) they often avoid going to certain places due to their child's behavior; and (g) the child's ASD condition and the child's daily care demands interfere too much in their social life.
At this level, there is a very high SPS.Parents of children with ASD are highly likely to endorse that: (a) they very often have difficulties with their work routine because they have no one to leave their child when they need to; (b) the child's daily care demands very often affect their work routine (e.g., missing work); (c) it is very difficult reconciling their work routine with the child's daily care demands; (d) when they go to parties or social events with their child, cannot have fun or interact with people; (e) they very often avoid going to certain places due to the child's behavior and comments aimed at their child, and (f) often or very often they are not invited to social events due to their child's behavior.
Note: b0, b1, b2, and b3 indicate the item's category after the regrouping presented in Table 3. OS denotes the overall SPS score computed by adding the responses of all 14 items in Table 1 (OS ranges from 14 to 55).

Social and Professional Satisfaction and the SPS-Scale
The professional and social satisfaction reported by parents in questions Q11 and Q12 (Table A.2, Appendix A) was negatively associated (p < 0.001) with the SPS-Scale (-0.37 and -0.52, respectively), indicating that the greater the satisfaction, the lower the SPS level.In addition, the self-assessment of stress in professional and social life addressed in questions Q13 and Q14 (Table A.2, Appendix A) was positively associated (p < 0.001) with the SPS-Scale (0.46 and 0.65, respectively).

Parental and Child Characteristics Predicting the Parents' SPS
Table 4 shows the linear regression results for the parental and child characteristics significantly associated with the parents' SPS.Primary caregivers' parents had a higher SPS level than parents who were not.Also, the higher the child's ASD symptoms, the greater the parents' SPS level.Fathers had a lower level of SPS than mothers, as did married participants compared to those with another marital status.A higher SPS level was suggested among parents of children aged 6-10 years than at other ages.

Discussion
The instrument proposed in this study calibrated 14 items adequately (Table 2).The SPS-Scale presented good psychometric properties and high internal consistency reliability, indicating that it is a valid psychometric instrument to assess the SPS experienced daily by parents of children with ASD.
According to Pereira et al. (2017), parents of children with ASD experience a significant impact on social and professional life.The SPS-Scale reinforces this finding since, in our study, 53.3% had SPS from moderate to very high levels.A fact that explains the parents' stress concerning social life is that their child's behavior makes them uncomfortable going to specific places.Also, prejudice usually generates discomfort (Minatel & Matsukura, 2014).On the other hand, parents' professional stress is usually related to difficulties with the work routine due to their child's care demands and the need to leave the professional career in the background (Veld et al., 2017).In this study, 36% of parents reported difficulties with their work routine because, in some situations, there was no one with whom to leave their child.Also, having to miss work, being late, or leaving early due to the child's demands was reported by 44%.Moreover, 75% reported that the child's daily care demands make them tired, interfering with the performance of their work activities.
The severity of ASD symptoms also predicted a higher parent's SPS level, corroborating other studies (Bitsika & Sharpley, 2017;Tomeny, 2017).According to the Diagnostic and Statistical Manual of Mental Disorders (APA, 2013), the ASD symptoms at middle and severe levels are the ones that generate the most difficulties and, therefore, more attention from caregivers is needed.
Mothers also had a higher level of SPS than fathers did, corroborating Kiami and Goodgold's (2017) finding, who reported a higher level of maternal stress.At the same time, McStay et al. (2014) and Miranda et al. (2019) reported a positive association between the child's behavior and parental stress, especially among mothers who assume the role of primary caregiver.In the present study, the primary caregivers' mothers also had a higher SPS level.It usually occurs because they have to assume greater responsibilities, modifying their daily life and distancing themselves from social life.They are also often forced to reduce their workload or leave the workforce as they cannot obtain appropriate childcare or a flexible work schedule (Pinto et al., 2016;Minatel & Matsukura, 2014).
A higher SPS level was also suggested among parents with children aged 6-10.It coincides with school-age children, a transition period that can be stressful and challenging for parents due to the communication and social interaction difficulties of their children with ASD (Connollya & Gersch, 2016;Adams et al., 2020).In contrast, a lower SPS level was indicated among married parents, corroborating the studies by Hasting (2003) and Tehee et al. (2009).This may be because sharing the child's daily care demands and concerns with a partner can better balance the home environment, reducing stress (Aguiar & Pondé, 2018).
In addition, parents classified as having very low or low SPS levels (46.7%) reported positive feelings.They are very satisfied (or satisfied) with their social life, and the child's ASD condition has little or no impact on their social life.The reason is that maintaining a social life and having the support of friends and family can positively affect the parents' well-being (Bluth et al., 2013).According to Ooi et al. (2016), some parents feel self-confident about raising a child with ASD.However, they face several difficulties in social life, including the lack of information from other people about ASD.Many people judge the child's behavior with ASD as bad behavior, which often bothers the parents and causes negative feelings.

Final Remarks
The SPS-Scale proposed in this study has proved beneficial in assessing the SPS experienced daily by Brazilian parents of children with ASD.However, it is noteworthy that our findings may not be generalized to all parents of children with ASD.As this is the first study examining the theoretical structure and psychometric properties of the SPS-Scale, its application in other similar and different cultures would be valuable in order to provide additional foundations for its use.

Figure 1 .
Figure 1.Analysis of the dimensionality of the 14-item instrument.PC: principal components and FA: factor analysis.
is the discrimination parameter and bk (k = 1, 2, 3) are the difficulty parameters.SE is the standard error.

Figure 3 .
Figure 3. Item trace plots for items P1 to S7 where each line reflects the probability of endorsing an item response category  given the level on the latent trait ( = 0, 1, …, ci -1, where ci is the number of categories of item i).The information curve of the SPS instrument is shown in the last plot on the right.

Table 1 .
The instrument for measuring the social and professional stress of parents of children with ASD Note: Items translated into the English language from the original Portuguese version.ASD: autism sprectrum disorder.

Table 2 .
Estimates of discrimination and difficulty parameters of each item Never -Rarely or Sometimes -0.49 (0.17)Often or Very often 2.04 (0.34) -

Table 3 .
The five levels of the SPS-Scale and their respective interpretations

Table 4 .
Regression analysis of the parental and child characteristics