Factor Analysis. Factor Analysis (FA) is not like the other techniques mentioned here, in the sense that it can not be used as a dimensionality reduction before a classifier. Its analysis stands on its own. FA is used to identify the structure underlying the variables and to estimate scores to measure latent factors themselves. In Factor Analysis, only the shared variance is analysed in contrast to PCA where all the observed variance is analysed. Furthermore, FA explicitly assumes the existence of latent factors underlying the observed data. PCA instead seeks to identify variables that are composites of the observed variables (Xxxx, s.d.). To conclude, the underlying factors in FA are labelable and interpretable compared to the uninterpretable PCA components (Xxxxxxx, 2019). Before FA is performed, it is important to evaluate whether there can be factors found in the dataset. Two tests that will be tried to check this are Xxxxxxxx'x Test and Xxxxxx-Xxxxx-Xxxxx (KMO) Test. Xxxxxxxx’x Test uses the correlation matrix against the identity matrix (i.e. ones on diagonals and zeroes elsewhere) to check if the observed variables have enough correlation between them. Ideally, the test is statistically significant. Meanwhile, KMO measures the adequacy both for each observed variable and the complete model by estimating the proportion of variance that might be a common variance among all observed variables. The values range between 0 and 1, with a value of 0.60 or above often considered as a good threshold. With a p value smaller than 0.0001 and a KMO of 0.766, FA may be performed. The first part of FA is choosing the number of factors. The Kaiser criterion can be used for this, which is very straightforward. All it does is only keeping the factors with eigenvalues greater than 1. In a standard normal distribution with mean 0 and standard deviation 1, the variance will be 1. Since the data is standard scaled, the variance of a feature is 1. This is the reason for selecting factors whose eigenvalues (variance) are greater than 1 i.e. the factors which explain more variance than a single observed variable. (Babu D., 2020) After this, FA is performed again with the correct amount of factors. Then, the loadings of each variable to each factor are checked to see which variables relate to which factors. To obtain these loadings, a rotation strategy is used so that the space with the loadings (represented as points) shows a clear pattern, i.e. factors that are clearly marked by high loadin...
Factor Analysis. To explore the different dimensions captured in each fatigue questionnaire and also assess their relationship with anxiety and depression, simple descriptive analyses were applied to the data, as well as Xxxxxxxx’x correlations. In this study, correlations of r≥0.6 are reported as strong correlations, r≥4 and <6 as moderate correlations and r<4 as weak correlations. Cronbach’s alpha was used to test the internal validity of the items in the fatigue questionnaires. Cronbach’s alpha is a coefficient of internal consistency which is commonly used as an estimate of the reliability of a psychometric test. Where validity is concerned with the extent to which an instrument measures what it is intended to measure. [Following this an exploratory factor analysis of the fatigue questionnaires was undertaken. A rotated factor matrix was performed with all the questions from each questionnaire as well as the fatigue VAS and the HADS scores. In order to identify the most appropriate questions and reduce down the number of items, all items which were not highly correlated were excluded (loading <0.6). To further reduce this both clinical interpretation and statistics were employed to exclude any very similar questions. The questions were the examined by the investigator and a second rheumatologist and using clinical judgement and after agreement between the two clinicians if two questions had almost identical wording or it was felt they were asking the same question then the question with the lowest loading was rejected and the question with the highest loading was retained. For example: I feel nervous and I feel tense were felt to be asking the same question. The loading into the factor analysis rotated factor analysis was 0.889 for I feel nervous and 0.672 for I feel tense; therefore, I feel tense was excluded from the final model. Consideration was also made to ensure that each dimension was represented.
