Item response analysis of the Geriatric Anxiety Inventory among the elderly in China: dimensionality and differential item functioning test

As the geriatric population increases, mental health of the elderly gains more and more substantial concerns, such as depression and anxiety. Prevalence estimates of anxiety disorders ranged from 3.2 to 14.2% in Switzerland and France, as reported in a comprehensive review of geriatric anxiety disorders [1]. Moreover, a survey in one city in China, Chongqing, indicated that 21.63% of older people suffered anxiety, especially among those with physical illness [2]. Though anxiety disorders are highly prevalent among older adults, screening instruments for the aged leave much to be desired [3]. Besides confusion with other disorders [4], cognitive deficits and somatic symptoms account together for the unsatisfactory validity of most measures [5, 6]. To overcome the above deficiencies, Pachana et al. developed the Geriatric Anxiety Inventory (GAI), especially for older populations [3].

The Geriatric Anxiety Inventory only has 20 brief items and facilitates studies regarding anxiety disorders of the elderly prominently. It features a dichotomous and single direction response format, which can decrease the cognitive load of respondents. It also involves minimal somatic symptoms, which helps distinguish mental disorders from somatic diseases [3]. Numerous studies have provided strong evidence for its desirability, with internal consistency ranging from 0.91 to 0.95 [3, 7], test-retest reliability ranging from 0.91–0.99 [3, 8] and good convergent validity [3, 9]. For probing DSM-IV Generalized Anxiety Disorder (GAD), a cut-point of 10/11 in the Geriatric Anxiety Inventory had a specificity of 84% and a sensitivity of 75, and 83% of patients were correctly classified [3]. In another study, an optimal cutoff of 9 was suggested, which had a 100% sensitivity and a 60% specificity, with 65% of participants correctly classified [10]. In short, the psychometric properties of GAI were proven to be excellent, which made it a promising screening and assessment of anxiety among the elderly.

Factor structure is essential in understanding, scoring, and interpreting the responses on the GAI [11]. The GAI was developed as a measure of a unidimensional construct [3, 12]. However, researchers have not reached a consensus on the factor structure of this instrument. The one-factor model was confirmed by Johnco et al. among 256 community-dwelling old adults in Australia [13], among older people living in Beijing communities [14] and among institutionalized old population in Portugal using both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) [15]. The unidimensionality was further supported by Molde et al. among psychogeriatric mixed in-and-out Norwegian patients using the bifactor analysis [11]. Although the one-factor model obtained most empirical support, two-, three-, and four-factor solutions also emerged in the current literature. A two-factor model was proposed by Ribeiro et al. based on the principal component analysis with varimax rotation on responses from a mixed sample of community-dwelling and clinical old adults [16]. Bendixen et al. found a similar two-factor solution among a sample of elderly with depression, dementia, or psychosis [17]. A three-factor model was first proposed by Márquez-González et al. among 302 old adults living in Spanish communities using principal-components analysis with varimax rotation [18]. Guan also obtained a similar three-factor among 1318 old adults living in Beijing communities with the same method [19]. Finally, a four-factor model was proposed by Diefenbach et al. among a mixed sample of 140 clinical and non-clinical old participants using principal components analysis [20]. These inconsistent findings regarding dimensionality of the GAI can be partly attributed to the analytic methods chosen: Traditional factorial analysis methods such as exploratory factor analysis (EFA) and principal components analysis (PCA) are mainly employed in those studies, and these methods may result in distorted results due to small size and unsatisfied assumptions [21, 22]. More recently, Molde et al. [23] resolved debates about the factor structure of the GAI with bifactor modeling in an extensive dataset with 3731 older adults from 10 national samples and found a primary unidimensional general factor of the GAI across nations.

Mokken scale analysis (MSA), a more sophisticated tool based on nonparametric item response theories, has been proposed to assess dimensionality [24, 25]. It is developed on the basis of the Guttman scaling model, which assumes that scale items are hierarchically ordered along levels of a latent construct. It is less restrictive concerning statistical assumptions and sample size than IRT models, such as Rasch model and logistic models. Compared to traditional factorial analysis, MSA has advantages in conducting dimensionality investigation and model evaluation at the same time, avoiding “difficult factors” and distortions due to item-score distributions. It is a better fit for discrete data sets [22]. The most general Mokken model, monotone homogeneity model (MHM) assumes unidimensionality, local independence, and latent monotonicity [24]. Moreover, the unidimensionality assumption of MHM contributed precisely to test the latent structure of an inventory through automated item selection procedure (AISP) [26, 27]. In a scale formed by Mokken analysis, the sum score of all items can be used as the indicator of the latent trait [24]. It is worth noting that the scale score is ordinal in nature, but it can be interpreted and used as interval values if ordinal transformations have no severe impact on the substantive interpretations of further statistical analyses [28]. Our study would adopt this method to provide complemental evidence to studies on the factor structure of the GAI.

Different groups of people may have different expressions of anxiety and depression. Previous studies indicated that females tended to report more anxiety symptoms than males did [29, 30], but this gender difference disappeared with age increasing [31]. However, before coming to these conclusions, measurement invariance needs to be justified: this instrument must measure the same anxiety symptom of the same extent in all groups [32]. Several researchers have realized the problem. They examined measurement invariance across sex and ages and found no item bias existed [11, 13, 33]. When developing the international translations of the GAI, researchers often have difficulties in finding the exact corresponding words in their languages. For example, the Portuguese version [16], the Spanish version [18], and the Chinese version [34] have different translations of the item “I have butterflies in my stomach” with the original Australia version [35]. In addition, Molde et al. pointed out that due to different understandings of the same item content, even the translation itself implied potential changes in the psychometric properties of the individual item and the whole scale [11]. It is still necessary to examine the item bias of the instrument in different cultures and languages.

Therefore, the present study had two aims: 1) to establish the factor structure of the GAI in a large Chinese sample using Mokken scale analysis [24, 25]; 2) to examine the measurement invariance of the instrument across different groups using DIF analysis.

The present study reevaluated the psychometric properties of the GAI among a large community-dwelling Chinese elderly sample. Mokken scale analysis was used to determine its dimensionality, and the logistic regression approach was used to detect differential item functions. Results revealed that the Chinese version of the Geriatric Anxiety Inventory possesses sound psychometric properties. It is unidimensional and has no item bias across sex and disease groups.

Previous studies have indicated conflicting findings regarding the factor structure of the GAI. Mainly based on exploratory factor analysis and confirmatory analysis, researchers have proposed one-factor solutions [11‐13, 15, 34], two-factor solutions [16, 17], three-factor solutions [18, 19], and a four-factor solution [20]. More recently, Molde et al. [23] addressed the contradictions about the dimensionality of the GAI using bifactor modeling and supported a primarily unidimensional structure across nations. To provide supplementary information about the factor structure debates, we introduced Mokken scale analysis, an NIRT based technique, to determine its dimensionality. Mokken scale analysis provides an effective procedure to determine the factor structure. Other than traditional factor-analytic methods, Mokken scale technique is capable of eliminating effects of the difference in individual item score frequency distributions [44] and provides a clear view on the items’ scalability [22]. Through observing the pattern of AISP, we could differentiate unidimensionality and multidimensionality. The results indicated that the GAI-CV was unidimensional, which supported the conclusion of Yan et al. [34]. Therefore, it is justified to use a simple sum score of the 20 items within the GAI-CV as a reliable index for anxiety among the elderly. It should be noted that the sum score is ordinal in nature, but it can be treated as interval data in case of no serious influence of ordinal transformations on interpretation of further statistical analyses. To our knowledge, this is the first time to explore the GAI with Mokken scale technique. Mokken scale analysis provides a comprehensive output about the scalability of items and the structure of scales [38]. The adoption of Mokken scale analysis in dimensionality test should be recommended in future studies of the GAI in different languages and cultures.

Measurement invariance of the GAI is very important, given researchers often make comparisons among groups with different sex, diseases, and cultures. Only Molde et al. have evaluated the differential item functions across sex, MMSE (The Mini-Mental State Examination) and MADRS (The Montgomery–Asberg Depression Rating Scale) groups. Their results indicated that no item had a substantial bias across those groups. We adopted the logistic regression method, which was one of the most effective and recommended ways to detect DIF [41, 45]. Logistic regression has many advantages over other DIF methods, such as the Mantel Haenszel. It does not require to categorize a continuous criterion variable, and it is capable of modeling both uniform and non-uniform DIF [46]. Previous studies have revealed that females tended to report more anxiety than males, and people with chronic diseases tended to be more anxious than those without somatic diseases. Our study verified that comparisons among those groups were reasonable, and the group differences on the GAI reflected substantial variability rather than differential item functions.

We acknowledged several potential limitations of this study. Although we conducted the analyses in a relative large representative sample, only old adults in Beijing communities were included. Therefore, the generalization of the conclusion to the elderly with various cultural and language backgrounds should be with caution. Future replications in diverse samples in other cultures and languages will be beneficial to the establishment of the worldwide adaptability of the GAI. Besides, our sample did not include clinical patients (e.g., older adults with a primary anxiety disorder). The generalizability of the findings is limited to those who are not clinically diagnosed with anxiety disorders. Future research should attempt to address the limitation of recruiting clinically disordered samples who met the criteria for a primary anxiety disorder.