Semi-sparse PCA

It is well-known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA). An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model/algorithm can act as a specific sparse PCA and as a low-rank-plus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new model, and the performance and behaviour of its algorithmic implementation

Sparse Exploratory Factor Analysis

Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional [Formula: see text]-norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods

Sparsest factor analysis for clustering variables: a matrix decomposition approach

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA

Mental distress in the general population in Zambia: Impact of HIV and social factors

<p>Abstract</p> <p>Background</p> <p>Population level data on mental health from Africa are limited, but available data indicate mental problems to represent a substantial public health problem. The negative impact of HIV on mental health suggests that this could particularly be the case in high prevalence populations. We examined the prevalence of mental distress, distribution patterns and the ways HIV might influence mental health among men and women in a general population.</p> <p>Methods</p> <p>The relationship between HIV infection and mental distress was explored using a sample of 4466 participants in a population-based HIV survey conducted in selected rural and urban communities in Zambia in 2003. The Self-reporting questionnaire-10 (SRQ-10) was used to assess global mental distress. Weights were assigned to the SRQ-10 responses based on DSM IV criteria for depression and a cut off point set at 7/20 for probable cases of mental distress. A structural equation modeling (SEM) was established to assess the structural relationship between HIV infection and mental distress in the model, with maximum likelihood ratio as the method of estimation.</p> <p>Results</p> <p>The HIV prevalence was 13.6% vs. 18% in the rural and urban populations, respectively. The prevalence of mental distress was substantially higher among women than men and among groups with low educational attainment vs. high. The results of the SEM showed a close fit with the data. The final model revealed that self-rated health and self perceived HIV risk and worry of being HIV infected were important mediators between underlying factors, HIV infection and mental distress. The effect of HIV infection on mental distress was both direct and indirect, but was particularly strong through the indirect effects of health ratings and self perceived risk and worry of HIV infection.</p> <p>Conclusion</p> <p>These findings suggest a strong effect of HIV infection on mental distress. In this population where few knew their HIV status, this effect was mediated through self-perceptions of health status, found to capture changes in health perceptions related to HIV, and self-perceived risk and worry of actually being HIV infected.</p

Working conditions, self-perceived stress, anxiety, depression and quality of life: A structural equation modelling approach

<p>Abstract</p> <p>Background</p> <p>The relationships between working conditions [job demand, job control and social support]; stress, anxiety, and depression; and perceived quality of life factors [physical health, psychological wellbeing, social relationships and environmental conditions] were assessed using a sample of 698 male automotive assembly workers in Malaysia.</p> <p>Methods</p> <p>The validated Malay version of the Job Content Questionnaire (JCQ), Depression Anxiety Stress Scales (DASS) and the World Health Organization Quality of Life-Brief (WHOQOL-BREF) were used. A structural equation modelling (SEM) analysis was applied to test the structural relationships of the model using AMOS version 6.0, with the maximum likelihood ratio as the method of estimation.</p> <p>Results</p> <p>The results of the SEM supported the hypothesized structural model (<it>χ</it>²= 22.801, <it>df </it>= 19, <it>p </it>= 0.246). The final model shows that social support (JCQ) was directly related to all 4 factors of the WHOQOL-BREF and inversely related to depression and stress (DASS). Job demand (JCQ) was directly related to stress (DASS) and inversely related to the environmental conditions (WHOQOL-BREF). Job control (JCQ) was directly related to social relationships (WHOQOL-BREF). Stress (DASS) was directly related to anxiety and depression (DASS) and inversely related to physical health, environment conditions and social relationships (WHOQOL-BREF). Anxiety (DASS) was directly related to depression (DASS) and inversely related to physical health (WHOQOL-BREF). Depression (DASS) was inversely related to the psychological wellbeing (WHOQOL-BREF). Finally, stress, anxiety and depression (DASS) mediate the relationships between job demand and social support (JCQ) to the 4 factors of WHOQOL-BREF.</p> <p>Conclusion</p> <p>These findings suggest that higher social support increases the self-reported quality of life of these workers. Higher job control increases the social relationships, whilst higher job demand increases the self-perceived stress and decreases the self-perceived quality of life related to environmental factors. The mediating role of depression, anxiety and stress on the relationship between working conditions and perceived quality of life in automotive workers should be taken into account in managing stress amongst these workers.</p

Initial validation of the mindful eating scale

Published Mindfulness, 2013, 5(6), pp. 719-729. The final publication is available at Springer via http://dx.doi.org/10.1007/s12671-013-0227-5Self-report scales for mindfulness are now widely used in applied settings, and have made a contribution to research, for instance in demonstrating mediation effects. To date there are no convincing data as to whether mindfulness skills generalise fully across life domains, and so some researchers have developed mindfulness scales for particular domains of behaviour. We present the development of a self-report scale to measure mindfulness with respect to eating behaviours