# Exploratory Factor Analysis.pdf

The Severe Asthma Questionnaire (SAQ) is a health related quality of life (HRQoL) questionnaire validated for use in severe asthma. It is scored using the mean value of 16 items (SAQ score) in addition to a single item global rating of HRQoL (SAQ-global). The aim was to validate clinically relevant subscales using exploratory factor analysis (EFA).

## Exploratory Factor Analysis.pdf

The SAQ was completed, along with measures of asthma control and EQ5D-5L by patients attending six UK severe asthma centres. Clinical data were included in the analysis. EFA using principal axis factoring and oblimin rotation was used to achieve simple structure of data.

There are two main forms of data extract: principal component analysis and factor analysis. Principal component analysis is a simpler and older form of analysis that became popular when computers were slower and is the default option in many statistical packages. Principal component analysis is a method of data reduction only, it does not distinguish between unique and shared variance and therefore does not identify causal factors (psychological constructs). The method risks overestimating variance. Factor analysis analyses only shared variance and in so doing provides information about underlying causal structures, it does not inflate estimates of variance and for most purposes is the recommended form of extraction [20]. We used factor analysis rather than principal component extraction because we wanted to identify causal constructs and estimate variance, and we used principal axis factor analysis as a commonly used type of factor analysis [20].

EFA is an exploratory tool that provides choice in the numbers of factors to be extracted. When used for subscale construction in HRQoL, the primary determinant of factor number and hence subscale number is a number that is both theoretically plausible and clinically useful. If that number produces a simple structure (see later), then that number can be accepted as the final solution. If that number fails to produce a simple structure, then alternatives should be considered. In our case, a plausible and useful number based on content is that there should be three factors, corresponding to activity, emotion and extra-pulmonary symptoms.

Once the number of factors is set, principal axis factoring coupled with rotation provides a solution capable of interpretation. The technique of rotation can be done either by forcing the factors to be uncorrelated (called orthogonal rotation, e.g., varimax) or allowing the factors to be correlated (called oblique rotation, e.g., oblimin, promax), each type of orthogonal or oblique rotation having slightly different properties. Orthogonal rotation should be used only when uncorrelated factors are predicted on theoretical grounds or when there is evidence from an earlier oblique rotation that the factors are largely uncorrelated. Varimax (i.e., orthogonal) rotation became popular through its use in psychology where there was a theoretical requirement for personality factors to be uncorrelated [22], but this form of rotation is often used incorrectly in situations where factors may be correlated. In the present case, factors are predicted to be correlated as the three content derived domains of the SAQ all form part of the overall HRQoL. Promax and oblimin are commonly used forms of oblique rotation, promax being computationally simpler than oblimin, oblimin being the preferred form [20] and that which was used here.

Although a HRQoL questionnaire may fail to provide validated subscales according to the criteria described above, the overall scale score can still be used. It is almost inevitable that all the items of HRQoL questionnaires will load on the first unrotated factor. This is because, in general, HRQoL deficits in a population increase with severity and so the first factor unrotated factor is simply a severity factor. An HRQoL item must by definition be related to health and it would be unusual if an item failed to correlate with overall severity. Subscale construct validation by EFA is more demanding as it requires specificity of items to constructs, rather than specificity to severity.

Following EFA, subscales were constructed on the basis of the factor loadings by taking the mean of items loading on any factor. The relationship between the subscales and other variables was examined using Pearson correlations. EFA and correlations were conducted using SPSS version 25. Tests of difference between correlations were carried out using Psychometrica ( ).

The night disturbance item cross-loads on the My Life and My Body factors, but males and females interpret the question differently. For females, the night disturbance item loads equally on the My Life and My Body factors, showing that for females night disturbance limits daily activity as well as adversely affecting bodily perceptions (e.g., fatigue and appearance). For males, night disturbance loads on the My Life factor and just misses significance on the My Body factor, indicating that for males the meaning of night disturbance is primarily, but not exclusively, in terms of limitation to daily activities. The night disturbance item (item 14) is scored to contribute to both the My Life and My Body subscales, consistent with the data from the total sample.

Despite evident weaknesses in EFA, the subscales of earlier asthma specific HRQoL questionnaires reflect a common distinction of activity versus emotions, a distinction consistent with the theory that HRQoL judgements are affected by two causes [24]. One cause is the underlying pathology that creates disease specific symptoms and creates activity limitation, thereby creating the meaning dimension reflected in the My Life subscale. The other is the underlying personality of the patient which creates mood disturbance, thereby creating the meaning dimension reflected in the My Mind subscale. Similar activity versus emotion distinctions are found in subscales are based only on content [2, 4] and in those using statistical analysis [4,5,6]. In the case of severe asthma, however, there is an additional group of items and meaning dimension relating to the impact of non-asthma symptoms. These symptoms arise partly due to the polysymptomatic nature of severe asthma [25] and partly due to side effects caused by treatment such as oral corticosteroids. Treatment varies with severity but some patients experience more side effects than others. The three factor solution provides a disease specific set of subscales, subscales that are consistent with guidelines that questionnaires and their subscales should be fit for purpose [1], this being something that is not achieved with five or six factor solutions [4, 5].

Although construct validity is an important part of subscale validation, the use of EFA for validating the overall score should be treated with caution. Items should not be selected on the basis of high factor loadings on a first factor as so doing can lead to overly restrictive set of items. Content validity through qualitative methods is an essential first step in establishing the items of a scale, as recommended by current guidelines [1]. Construct validation of subscales is carried out only after content validity is established. Although cross-loading items can be removed, such removal has the potential to weaken the breadth of the questionnaire.

Exploratory factor analysis (EFA) is one of the most widely used statistical procedures in psychological research. It is a classic technique, but statistical research into EFA is still quite active, and various new developments and methods have been presented in recent years. The authors of the most popular statistical packages, however, do not seem very interested in incorporating these new advances. We present the program FACTOR, which was designed as a general, user-friendly program for computing EFA. It implements traditional procedures and indices and incorporates the benefits of some more recent developments. Two of the traditional procedures implemented are polychoric correlations and parallel analysis, the latter of which is considered to be one of the best methods for determining the number of factors or components to be retained. Good examples of the most recent developments implemented in our program are (1) minimum rank factor analysis, which is the only factor method that allows one to compute the proportion of variance explained by each factor, and (2) the simplimax rotation method, which has proved to be the most powerful rotation method available. Of these methods, only polychoric correlations are available in some commercial programs. A copy of the software, a demo, and a short manual can be obtained free of charge from the first author.

Exploratory factor analysis is a complex and multivariate statistical technique commonly employed in information system, social science, education and psychology. This paper intends to provide a simplified collection of information for researchers and practitioners undertaking exploratory factor analysis (EFA) and to make decisions about best practice in EFA. Particularly, the objective of the paper is to provide practical and theoretical information on decision making of sample size, extraction, number of factors to retain and rotational methods.

The questionnaire resulted from literature search, on-site observation and cognitive interviews. It was applied in 2006 to a sample of 201 enrollees of five home care programs in the city of Thessaloniki and contains 31 items that measure satisfaction with individual service attributes and are expressed on a 5-point Likert scale. The latter has been usually considered in practice as an interval scale, although it is in principle ordinal. We thus treated the variable as an ordinal one, but also employed the traditional approach in order to compare the findings. Our analysis was therefore based on ordinal measures such as the polychoric correlation, Kendall's Tau b coefficient and ordinal Cronbach's alpha. Exploratory factor analysis was followed by an assessment of internal consistency reliability, test-retest reliability, construct validity and sensitivity. 350c69d7ab

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