Factor Structure and Measurement Invariance of the Perceived Social Support Scale in Women Diagnosed with Breast Cancer

Background: The perceived social support of breast cancer patients has a great effect on regulating their negative emotions such as anxiety and depression, which is helpful to improve their mental health level. The Perceived Social Support Scale (PSSS) is a frequently used instrument designed to assess the degree of perceived social support. However, the psychometric properties of PSSS in breast cancer patients have not been adequately studied. The purposes of this study were to evaluate the factor structure of PSSS and examine its measurement invariance across different demographic variables in a sample of breast cancer patients. Method: This study involved 989 female patients diagnosed with breast cancer, aged from 25 to 72 years old (Mean age = 47.67 years, SD = 8.87). The single-group conrmatory factor analysis was administrated to examine the factor structure of PSSS. The multi-group conrmatory factor analysis was used to demonstrate the measurement invariance of PSSS across different sociodemographic variables. Results: The PSSS had satisfactory reliability and validity in current sample. The three-factor model t well in the overall sample and population subgroups. Congural, metric, scalar, and strict invariances were all supported by the data of breast cancer samples across different age, places of residence and educational levels. Conclusion: This study examined the factor structure and measurement invariance of PSSS across different demographic variables in women diagnosed with breast cancer. Our results proved that PSSS is suitable for use among breast cancer patients. This study provided preliminary evidence for the factor structure and measurement invariance of PSSS across different demographic variables in women diagnosed with breast cancer. Our results proved that PSSS is a three-factor structure scale with good validity and reliability. In addition, the measured invariance results suggest that PSSS can be used in breast cancer patients of different ages, education levels, and places of residence. This property of the scale will ensure the accuracy of results comparison between different groups in future studies.


Background
Breast cancer is a disease of global concern due to its high incidence and rising mortality. According to the 2018 Global Cancer Statistics Report [1], the number of newly diagnosed breast cancer cases worldwide reached 2.1 million, accounting for about a quarter of the total number of new cases of female malignant tumors. Breast cancer is the most commonly diagnosed cancer in the vast majority of the countries and is becoming a leading cause of cancerborne death in women. The diagnosis and treatment of breast cancer will be psychologically strenuous and may lead to severe psychological distress to patients [2]. Due to adverse effects of breast cancer treatment, patients are often accompanied by negative emotions such as anxiety and depression [3]. Social support has played a vital role in the treatment of breast cancer patients. Studies have shown that breast cancer patients receive support from their spouses, family, friends and colleagues, which makes them feel loved and cherished, and can help to promote posttraumatic growth [4].
Social support can be divided into objective support and subjective support [5]. Objective support refers to visible, and practical support, including direct material assistance and the existence as well as the participation of group relations [6]. Subjective support is also known as perceived social support, which stems from an in-depth research on social support, and which re ects the emotional experience and evaluation of the degree of external support [6]. In the last few decades, several qualitative and quantitative scales were developed to measure social support. The Perceived Social Support Scale (PSSS) was one of the most extensively used scale, which was developed by Zimet [7] et al to provide the quantitative measurement of individuals' perceptions of social support from family, friends and signi cant others. This scale had several advantages. With just 12 items, it was simple and easy to operate. Unlike other similar tools, it could also measure support in multiple areas. The Perceived Social Support Scale has been translated into multiple languages, such as: Chinese version [8]; French version [9]; Turkish version [10][11][12][13]; Portuguese version [14,15]; Spanish version [16,17], etc. Many studies had shown that this scale exhibited excellent psychometric properties in different cultures and were widely used in different countries [18][19][20][21]. It can be applied not only to healthy people but also to various clinical patients such as diabetes [22], breast cancer, autism and mental disorders. In brief, the PSSS is an adaptable instrument for evaluating perceived social support in a variety of samples. Moreover, many scholars had explored the factor structure of the PSSS and con rmed the three-factor structure, named as support from family, friends and other aspects [9,[23][24][25]. There were a few scholars believed that the two-factor model can also be applicative, which divided the source of support into family support and other support sources [8,26].
Perceived social support may help breast cancer patients to adjust their state of mind in the face of stressful life events. There have been numerous previous clinical studies on perceived social support for women with breast cancer [27][28][29]. To the best of our knowledge, no studies had been conducted to examine the factor structure and measurement invariance of the PSSS in women diagnosed with breast cancer.
Uncertain factor structure of research tools may lead to biased research results. Therefore, it is very necessary to con rm the factor structure of the PSSS in speci c participants. With this in mind, one of our research purposes was to examine the most applicable factor model of the PSSS in Chinese women who were diagnosed with breast cancer.
In addition, according to previous studies, breast cancer patients with different sociodemographic variables were found to have different levels of reporting social support scores. For example, Kim and Jang [30] found that the level of perceived social support among breast cancer patients differed signi cantly in educational background. Sammarco [31] demonstrated that younger breast cancer patients reported signi cantly more perceived social support than older ones. Another study showed that patients who lived in cities had signi cantly higher PSSS scores than those who lived in rural areas [32]. However, if we want to prove that these comparative results are reliable, we need to prove the measurement invariance of the PSSS in the patients diagnosed with breast cancer. In other words, invariance is a prerequisite for the comparison of differences between different groups. As far as we know, there are currently no research that can be used as evidence of the measurement invariance of PSSS in different sociodemographic variable groups of breast cancer patients. It prompted us to do more research in this study to evaluate the measurement invariance of the PSSS in a sample of breast cancer patients across different demographic variables (age, places of residence and educational levels).
In all, the purposes of this work were to: (1) evaluate the construct validity of PSSS in women diagnosed with breast cancer; (2) test the factorial invariance of PSSS using a range of demographic variables (age, places of residence and educational levels).

Participants
During the period from March 2011 to March 2016, we recruited 1030 female patients who had been diagnosed with breast cancer from two hospitals in Hunan Province of Mainland China to participate in this study. Patients with a known history of major psychiatric disorder or substance abuse were excluded. All the data had been checked. Of 1030 patients who agreed to take part in the study, 11 (1.1%) patients were excluded due to data missing on most items of the PSSS. In addition, 13 (1.3%) patients did not report their ages, 17 (1.7%) patients did not report years of schooling, and were thus eliminated. The nal analytic sample consisted of 989 female patients with breast cancer.
All patients participating in this study were well informed of the content and con dentiality policy. All participants voluntarily signed an informed consent form.

Instruments
The Chinese version of the Perceived Social Support Scale (PSSS) was used in this study. It was used to evaluate the degree of support from various social support sources that an individual felt and understood. The PSSS contained 12 items re ecting three sources of support (family, friends and signi cant others). The scale was scored on a sevenpoint Likert-type scale that ranged from 1 (very strongly disagree) to 7 (very strongly agree). The higher the score of each dimension and the total table, the higher will be the degree of social support that the individual understood. In this study, Cronbach's alpha of the whole scale was 0.95, showing high internal consistency.

Procedure
The study was carried out in hospital wards. Participants received a copy of the printed questionnaire immediately after providing informed consent. All participants were requested to ll up the self-report questionnaire on the spot. There was an experienced psychology student nearby who could provide professional assistance if they had some questions about the questionnaire.

Data analysis
SPSS version 22.0 and Mplus version 7.0 were used to calculate descriptive statistics and conduct item analyses in this study [33].
Firstly, in order to determine the optimal factor structure of the PSSS in the breast cancer population, single-group con rmatory factor analysis (CFA) was administrated to verify the three-factor model and two-factor model of PSSS. At the same time, we can evaluate the construct validity of the scale. Considering the non-normality of the data, all the measurement models were estimated using the maximum likelihood estimation with standard error and meanvariance corrected chi-square test statistics (MLMV) [34]. Because of the sensitivity of the chi-square (χ 2 ) test statistic to sample size [35], the following goodness-of-t indexes were used to evaluate the adequacy of the model t to the data, including the chi-square/degree of freedom (χ 2 /df), the comparative t index (CFI), the Tucker-Lewis index (TLI), the Bayesian information criterion (BIC), standardized root mean square residual (SRMR), and root mean square error of approximation (RMSEA) with a 90% con dence interval (CI). Generally, CFI ≥ 0.90, TLI ≥ 0.90, SRMR ≤ 0.08 and RMSEA ≤ 0.08 can indicate an acceptable model t [36]. The model with larger CFI and TLI as well as smaller RMSEA and BIC values was the most appropriate.
Secondly, the multigroup con rmatory factor analysis method was applied to test the measurement invariance of PSSS across age (younger and older), levels of education (lower and higher), and places of residence (rural and urban). A series of hierarchically nested models were tested, including con gural, metric, scalar, and strict invariance models [37]. Every model represented a speci c level of measurement invariance, ranging from minimum invariance to maximum invariance. There is a progressive nesting relationship between different levels of invariance. Con gural invariance (Model 1) was used to determine whether the factor structure tted each group in the same manner. It was an initial analysis with no constraints, with the factor loadings, intercepts of variables and error variances being set free. Metric invariance (Model 2) was used to gauge whether factor loadings were similar in both groups. In this model, the constraints of equivalent factor loadings were imposed, and the intercepts of variables and error variances were freely estimated. Scalar invariance (Model 3) was used to assess whether factor loadings and intercepts were similar in both groups. The factor loadings and intercepts of variables were constrained to be equal across age, levels of education, and places of residence. Strict invariance (Model 4) was used to test whether factor loadings, intercepts and the error variances between different groups were similar. The factor loadings, intercepts of variables and error variances were all set to be equal across age, levels of education, and places of residence. Posterior models were nested on the former one. Only when the former model was set up, the next model was allowed to be done.
In order to evaluate invariance between consecutive models, the ΔCFI and ΔRMSEA were examined. A ΔCFI value of less than 0.01, a ΔRMSEA value of less than 0.01 and a smaller BIC value were considered to be evidence of invariance [35], given that the values have been widely used and supported in recent researches [38,39].

Descriptive Statistics
A total of 989 female patients diagnosed with breast cancer participated in the study. The age of these participants ranged from 25 to 72 years old (Mean age = 47.67 years, SD = 8.87). The vast majority of participants (93.5%) were married women. A few patients are divorced (3.3%), or widowed (2.8%), or single (0.3%). The years of education of these participants ranged from 0 to 19 years (Mean year = 10.12 years, SD = 3.57). The patients from urban and rural areas each accounted for about half of the sample size. All patients participating in the questionnaire were receiving breast cancer treatment. 23.5% of patients were receiving chemotherapy before mastectomy; 70.9% of patients had just nished mastectomy and were undergoing chemotherapy; 5.6% of patients were receiving rehabilitation after mastectomy. The detailed basic information of the patient was presented in Table 1. The descriptive data of the scale scores were shown in Table 2.

Single Group Con rmatory Factor Analyses
Firstly, the data tting of the three-factor model and two-factor model were tested in the total sample. The t indices of the two factor structure models in the total sample were listed in Table 3. that the CFI and TLI of the three-factor model were larger and the RMSEA and BIC were smaller, the three-factor model outperformed the two-factor model in the total sample. Furthermore, we conducted the CFAs for groups of different age, places of residence, and education levels. The t indices of CFA in demographic subgroups were concluded in Table 3. According to the tting indices, the three-factor model t the data of each sub-sample well, while the twofactor model showed poor tting degree and was not suitable. In summary, the data tting performance of the threefactor model was better than that of the two-factor model, whether in the overall sample or in different sociodemographic variable subgroups. Therefore, the three-factor model could be used as the initial model for subsequent tests. As shown in Table 4, the standardized factor loading of each item in the three-factor model of the PSSS was above 0.70, ranging from 0.794 to 0.967. The latent correlations between the factors in the total sample were showed in Table 5. All correlations were statistically signi cant.  Factor I, family support; Factor II, friends support; Factor III, other support.
All correlations with "**" are statistically signi cant at p 0.01 level.

Measurement Invariance of PSSS Three-Factor Model Across Demographic Groups
We evaluated the PSSS measurement invariance across different age groups (under 45 years old and over 45 years old). Con gural invariance did not set any parameters to constrain different age groups. All indicators met the tting requirements, indicating that the scale supported con gural invariance. Therefore, this paradigm was used as the baseline model for subsequent nested models. Next, we checked the metric invariance model and set the model parameters so that the factor loading is equal between different age groups. Comparing with the previous model, we could nd that ΔCFI and ΔRMSEA were 0.002, and BIC value reduced by 32.103, which proved that the model supported metric invariance. Consequently, when testing breast cancer patients of different ages, every item of PSSS represented the same meaning. In the next step, the intercept was speci ed to be equal between the older group and the younger group. Compared to the metric invariance model, CFI did not change, RMSEA changed by 0.002, and BIC decreased by 54.380, which demonstrated the su ciency of the scalar invariance. Thus, the strict invariance test could be continued. We limited the error variance to be equal between the older and younger groups. On the basis of the scalar invariance model, CFI changed by 0.002, RMSEA changed by 0.006, and BIC decreased by 44.127. The results con rmed the assumption of strict invariance.
To assess the PSSS measurement invariance in different places of residence, patients were divided into urban and rural groups according to their usual residence. We tested the con guration, metric, scalar, and strict invariance between the two groups in turn. We found that all the invariance models t the data well. The values of CFI and TLI in each model were greater than 0.9. The values of RMSEA and SRMR were also within a reasonable range. When each model was compared with the previous model, all ΔCFI were 0.001, and the value of BIC were also successively reduced. RMSEA decreased by 0.002 from the con guration invariance model to the metric invariance model, by 0.002 from the metric invariance model to the scalar invariance model, and by 0.005 from the scalar invariance model to the strict invariance model. Therefore, the data satis ed the strict invariance model.
In the end, the measurement invariance of different educational levels was evaluated. According to patients' years of education, women were divided into two groups with lower education level (less than or equal to 9 years) and higher education level (more than 9 years). In each step of the invariance test, all indicators met the model requirements.
Comparing each model with the stricter constraint model, ΔCFI and ΔRMSEA were both less than 0.01. Table 6 summarized the tting indexes of the measurement invariance model under different restricted conditions. In conclusion, it was satisfying that PSSS met the strict invariance model among different ages, education levels and residential groups.

Discussion
PSSS is a tool widely used to measure the degree of perceived social support in the general and clinical population.
This current study con rmed the construct validity and measurement invariance of the PSSS in a sample of women diagnosed with breast cancer. This investigation contributed to the empirical research of PSSS in some aspects.
First of all, the results of this research veri ed again the three-factor structure of PSSS, which was consistent with previous ndings [7,[40][41][42]. The study had shown that the three-factor structure of PSSS was better than the twofactor structure in female samples with breast cancer. The three-factor model of PSSS provided an appropriate t for the overall sample of and the data in each demographic variable group. Based on the above results, the three-factor structure of PSSS can be used as a baseline model for further research on the measurement equivalence of the scale.
In order to determine the measurement invariance of PSSS in the breast cancer population, we established the multigroup models. Four models were evaluated in turn for each demographic statistical variable. Every model had an increasing level of restrictiveness. The results showed that the con gural invariance, weak invariance, strong invariance, and strict invariance of PSSS were all supported by the data of breast cancer samples. With the increasing number of equal constraints between groups, the model did not change signi cantly, and the main psychometric characteristics were not sacri ced. Therefore, the PSSS scale had cross-group stability and was suitable for breast cancer patients with different sociodemographic variables. The establishment of con gural invariance indicated that the PSSS measurement of different sociodemographic variable groups can re ect the same number of factors and factor patterns. Moreover, The establishment of weak invariance indicated that the relationship between observed variables and latent variables of PSSS was equivalent among different groups. Every observation item of the scale had the same unit among different groups. Every time the latent variable changes by one unit, the observed variable will have the same degree of change in different groups. The scores of perceived social support between different groups can be directly compared and explained. The same score represented the same meaning. Satisfying strong invariance meant that the cross-group difference in the mean of the observed variable can estimate the difference between the groups in the mean of the latent variable. The comparison of perceived social support among breast cancer patients of different ages, places of residence, and different levels of education was meaningful. Strict invariance showed that the measurement error caused by random factors and the variance of the latent variable were equal among groups. The difference in the scores of the Perceived Social Support Scale at different ages, different levels of education, and different places of residence can be explained by latent variables.
Like other studies, our research had some limitations. We only divided the age stage and education stage into two groups, which can be divided into more detailed groups for further research in the future. Besides, this study is a crosssectional study, without a long-term follow-up survey of patients. Therefore, we cannot evaluate the longitudinal invariance of PSSS over time in breast cancer patients. Further research is needed to determine the characteristics of PSSS scores over time. Finally, PSSS was widely used in clinical practice, yet this study made use of only women with breast cancer as samples. Consequently, the measurement invariance of PSSS under different sociodemographic variables in other clinical patients and healthy people remains to be examined.
In short, we explored the construct validity and psychometric characteristics of PSSS in female breast cancer patients.
Despite the above limitations, taking into account the clinical signi cance, all equivalence models of different degrees can be accepted, and the comparison between different ages, education levels, and residences at the level of the observed variables (total or average score) is meaningful. Therefore, it has good application value in large-scale investigation and research and clinical diagnosis.

Conclusions
This study provided preliminary evidence for the factor structure and measurement invariance of PSSS across different demographic variables in women diagnosed with breast cancer. Our results proved that PSSS is a threefactor structure scale with good validity and reliability. In addition, the measured invariance results suggest that PSSS can be used in breast cancer patients of different ages, education levels, and places of residence. This property of the scale will ensure the accuracy of results comparison between different groups in future studies. China, and all patients who participated in the study with written informed consent.

Consent for publication
Written informed consent for publication was obtained from all participants.

Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests
The authors declare that they have no con ict of interest.     Factor I, family support; Factor II, friends support; Factor III, other support.
All correlations with "**" are statistically significant at p 0.01 level. RMSEA, root mean square error of approximation; CI, confidence interval; BIC, Bayesian information criterion; Δ, change in the parameter.