Measurement Invariance of the New Sexual Satisfaction Scale short form

The objective was to assess the incremental validity, internal consistency and temporal stability of the New Sexual Satisfaction Scale short version (NSSS-S) in Span-ish-speaking Latino adults. The sample included 401 university students (232 women and 169 men), sexually active, 18 to 38 years old (M = 20.83; SD = 2.66). A subsample of 76 participants answered the scale four weeks after the first application. Confirmatory factor analysis (CFA) identified a two-factor structure. The invariance analysis with multi-group confirmatory factor analysis (MGCFA) confirmed the invariance by sex of the scale. The internal consistency reliability of the scale and its subscales was excellent for both men and women ( ω = .89 - .95) and the temporal stability, four weeks after the first application, was adequate ( r = .74; ICC = .85). Finally, men scored higher in overall sexual satisfaction and the Ego-Centered subscale, but not in the Partner -and Sexual Activity-Centered subscale, as compared to women. To conclude, the NSSS-S is a psycho-metrically appropriate scale to measure sexual satisfaction in Spanish-speaking Latino adults.


Introduction
Sexual satisfaction (SS), the last phase of the human sexual response (Carrobles & Sanz-Yaque, 1991) refers to the subjective assessment of liking or disliking that people make about their sexual relationships and includes the pleasant sensations derived from the physical act that are related to the emotional satisfaction of the individual in order to find confidence and self-confidence (Ahumada, Luttges, Molina, & Torres, 2014;Lawrance & Byers, 1995). High levels of SS are associated with higher global quality of life and self-esteem, and less depression, anxiety, stress, physical health problems, and poor self-concept; furthermore, both, self-esteem and body image predict SS (for a review, see Sánchez-Fuentes, Santos-Iglesias, & Sierra, 2014).
The PSSI (Pinney et al., 1987) and the SSS-W (Meston & Trapnell, 2005) are scales designed to assess SS for women only. The first evaluates the general SS and the SS with the partner; the second evaluates two relational domains (communication and compatibility) and three interpersonal domains (feelings of inner happiness, concern for relationship, and personal concern) of women´s SS. The ISS (Hudson et al., 1981) is a one-dimensional scale that assesses the degree, severity, and magnitude of relationship problems in the sexual component. However, the ISS was built based on the clinical and personal experience of the author, so its construct validity is questionable. The GRISS (Rust & Golombok, 1986) is a measure of the existence and severity of sexual dysfunctions (e.g., impotence, anorgasmia, premature ejaculation, and vaginismus), designed for heterosexual couples. The GMSEX (Lawrance & Byers, 1995) evaluates the overall SS; however, the scale is restricted in terms of variance, since the measurement is made from an item and its reliability is limited (Mark, Herbenick, Fortenberry, Sanders, & Recee, 2014). The ESSS (González-Rivera et al., 2017) is a multidimensional scale that evaluates the perception of sexual life, negative feelings after sexual activity, perceived sexual performance, and the individual role during sexual intercourse. However, the ESSS focuses on the evaluation of the SS centered on the person.
The NSSS (Štulhofer et al., 2010) is a useful instrument to assess SS and is based on the theory of Bancroft, Loftus, and Long (2003) called three windows. The authors evaluated the scale in diverse samples: adults and young, men and women, heterosexual and different sexual orientation, clinical and community samples. The NSSS can be used for research in non-clinical settings.
Originally the NSSS (Štulhofer et al., 2010) included 20 items. The principal component analysis (PCA) with oblimin rotation derived two dimensions: The Ego-Centered subscale, devoted on personal experiences and sensations (e.g. quality and frequency of one´s sensations, orgasms, and sexual excitement) and the Partner -and Sex-ual Activity-Centered subscale (e.g. trust, commitment and emotional closeness with a partner). The authors evaluated the internal consistency in two student samples, two community samples, and one sample of Croatian non-heterosexual adults, and reported Cronbach´s alpha indices of ≥ .94 for the full-scale and ≥ .90 for both subscales and the short version.
In a later study, Štulhofer, Buško and Brouillard (2011) derived a short version (NSSS-S), which includes 12 Likert-type items (1 = Not at all satisfied to 5 = Extremely satisfied). The PCA with oblimin rotation derived a factor that measures personal and partner sexual satisfaction, regardless of gender, sexual orientation, or marital status.
The NSSS-S was recently translated and adapted for adult women and men in Spain (Strizzi et al., 2016). The principal axis factoring extraction with promax rotation derived two factors. Confirmatory factor analysis (CFA) proved the existence of two factors. It should be noted that factor validity for the NSSS-S has not been evaluated in Spanish-speaking Latino adults. Furthermore, the invariance by sex for this scale has not been studied. Note. χ 2 = Chi square; SCF = scaling correction factor for MLR; df = degrees of freedom; p = significance; RMSEA = root mean square error of approximation; CI = confidence interval; SRMR = root mean square residual; CFI = comparative fit index; TLI = Tucker-Lewis index.
Finally, previous studies have used Cronbach's alpha coefficient to assess the internal consistency of the scale. However, some authors have pointed out that the Cronbach's alpha coefficient has some limitations, for example, it is affected by the number of items, the number of response options, and the proportion of the variance (Domínguez-Lara & Merino-Soto, 2015). Therefore, it has been suggested to include more adequate indices for calculating the internal consistency of scales of an ordinal nature. In this sense, this study aimed to evaluate two previously identified factorial models for the NSSS-S (Mark et al., 2014;Štulhofer et al., 2011), in Spanish-speaking Latino adults using CFA. It also aimed to assess the incremental validity, the internal consistency and the temporal stability of the scale using multi-group confirmatory factor analysis (MGC-FA) and finally, to compare the SS between men and women.

Methods Participants
The sample included 401 university students (232 female and 169 male), sexually active, from 18 to 38 years old (M = 20.83; SD = 2.66) selected by non-probability convenience sampling, selected from two public universities in the municipality of Nezahualcoyotl, State of México. A subsample of 76 participants answered the scale four weeks after the first application.

Procedure
The present study followed the ethical principles of the Declaration of Helsinki (World Medical Association, 1964) for medical research involving human subjects. After receiving informed consent, participants were notified of the purpose of the study and proceeded to answer the scale in their classroom.

Data analysis
Multivariate normality analyses (Mardia, 1970) were performed using the R software (R Core Team, 2013). Absolute values of > 5 and a p < .05 were indicative of non-normality.
All confirmatory analyses were performed with Mplus 8.0 software (Muthén & Muthén, 2017). Given the discrepancies in the underlying structure of the NSSS-S, we did not use the one-dimensional structure proposed by Štulhofer et al. (2011), instead, we tested two models: one-dimensional (Štulhofer et al., 2011) and bifactorial (Mark et al., 2014). To assess the fit of the model, two absolute fit indices were used: 1) the Satorra-Bentler scaled chi-square (S-B χ 2 /df) and 2) the standardized root mean square residual (SRMR). Additionally, two comparative adjustment indices were used: The comparative fit index (CFI) and the Tucker-Lewis index (TLI); and a parsimonious adjustment index, the root mean square error of approximation (RMSEA). To consider that the model has a proper fit, values less than 2 indicate good fit and values between 2 and 3 indicate acceptable fit for the S-B χ 2 /df index (Schermelleh-Engel, Moosbrugger, & Müller, 2003); for the SRMR index, values less than .05 are indicative of a good fit (Hooper, Coughlan, & Mullen, 2008); for CFI and TLI, values > .95 are interpreted as a good fit (Hu & Bentler, 1999); and for the RMSEA, an index between .05 and .08 is considered as a reasonable adjustment (Browne & Cudeck, 1993).
The analysis of invariance by sex with MG-CFA included the examination of the configural invariance, the metric invariance, the scalar invariance, and the residual or strict invariance. To evaluate the incremental models, the Cheung and Rensvold (2002) criteria were used: ΔRMSEA ≤ .015 and ΔCFI ≤ .01.
To calculate the internal consistency of the scale, McDonald´s (1999) coefficient omega (ω) was used, which works with factor loads, which reduce the risk of overestimating reliability since it does not depend on the number of items and can be used in continuous variables. The values of ω can be interpreted as: unacceptable (< .70), fair (.70 -.79), good (.80 -.89) and excellent (≥ .90;Cicchetti, 1994).

Confirmatory factor analysis
The CFA was performed to evaluate the fit of two models: one-dimensional and bifactorial (F1 = items 1-6; F2 = items 7-12). As shown in Table 1, the two models have adequate fit indices, although Model 2 presents better fit indices. After inspecting the modification indices, we released covariance errors between items 11 and 12, thus, improving the fit. For this model, the item-total correlations ranged from .71 to .82. The items loaded significantly in their respective factor (p < .0001) and ranged from .69 to .83. Subsequent analyses were performed using the re-specified two-factor model (F1 = items 1-6; F2 = items 7-12).

Invariance analysis by sex
We first evaluated the fit of the re-specified model for each group (men and women). As shown in Table 2, the fit was acceptable for women and good for men. For the configural invariance, the measure of model fit was good. Furthermore, the changes in CFI and RMSEA indicate that the NSSS-S is invariant for sex, therefore, the scale can be applied to men and women.

Internal consistency
The omega coefficient indicated that the 12 items of the NSSS-S show good internal consistency for the whole sample, for both men and women (Table 3).

Temporal stability analysis
A subsample of 76 participants answered Note. Pearson and intraclass coefficients were significant (p = .0001).
the NSSS-S four weeks after the first application. Temporal stability analysis showed low Pearson and ICC correlations for men compared to women on the scale and its two subscales (Table 3).

Discussion
The purpose of this study was to assess the incremental validity of the NSSS-S. To our knowledge, this is the first study to focus on this aspect of the scale. Therefore, after re-specifying the model, the invariance by sex was tested. The NSSS-S showed metric, scalar, and strict invariance. These findings indicate that the construct represented by the NSSS-S is the same for university men and women, and the scores and means of the NSSS-S can be compared between these groups.
Although there are various instruments to evaluate SS (González-Rivera et al., 2017;Hudson et al., 1981;Lawrance & Byers, 1995;Meston & Trapnell, 2005;Pinney et al., 1987;Rust & Golombok, 1986), the NSSS-S has a theoretical framework and allows evaluating personal SS as a couple, regardless of gender, sexual orientation or marital status. Furthermore, the scale can be used in non-clinical settings. However, studies have reported inconsistent results regarding the factor structure of the NSSS-S. Some authors have found that the scale is unifactorial (Hoy et al., 2019;Štulhofer et al., 2011), and others point out that it is bifactorial (Mark et al., 2014;Santos-Pechorro et al., 2016;Strizzi et al., 2016). Our results support the two-factor structure of NSSS-S.
Most previous studies have evaluated the internal consistency of the NSSS-S using the Cronbach's alpha coefficient. In this study, internal consistency was assessed using the McDonald's omega coefficient (1999), which allows a more precise estimation of the internal consistency of the items and reduces the effect of the number of the items included in the scale. Consistent with the findings of previous studies (Hoy et al., 2019;Mark et al., 2014;Santos-Pechorro et al., 2016;Strizzi et al., 2016;Štulhofer et al., 2011), our findings support the internal consistency of the NSSS-S and its subscales for both men and women. Furthermore, the scale has adequate temporal stability, which is also consistent with previous studies (Mark et al., 2014;Štulhofer et al., 2011).
In gender comparisons, our findings are consistent with previous studies (for a review, see Petersen & Hyde, 2010), which indicate that SS is higher in men than in women. These results support the conclusions of Hyde (2005) about gender differences in sexuality. Also, each society has different criteria to value sexuality, being that men have greater sexual freedom as compared to women (Grindell, 2009).
Finally, the findings of this study indicate that the NSSS-S is a two-dimensional measure that allows evaluating SS in Spanish-speaking Latino adults. The scale has incremental validity, adequate internal consistency, and temporal stability.

Limitations
Despite the contribution of this study, we can highlight some limitations, for example, the sample was recruited from only two public universities, which could be unrepresentative of adults from other Spanish-speaking cities, so future studies could include samples representative of other Spanish-speaking regions and may even include older adults.
SS studies have mainly been focused on heterosexual people (Sánchez-Fuentes & Sierra, 2015). Another limitation of this study was that it did not include a sample of participants with different sexual orientation, so this aspect should also be addressed in future studies with Hispanic-Latino populations.
In addition, future studies could assess the invariance of this scale, according to the body mass index and the marital status of the participants, which are variables associated with SS. Furthermore, in this study it was not possible to cross-validate the re-specified model using a new sample, which would represent another contribution to the incremental validity of the scale.
Finally, a further limitation of this study was that convergent and divergent validity of the scale were not evaluated.