Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using artificial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the theoretical and finite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of di¤usion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model.

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework. We present here a possible solution based on factor analysis of compositions illustrated with a case study. We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members. We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except fertilisers due to the heterogeneity of their composition. This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are intrinsic to the relative nature of compositional data

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data

Exploratory factor analysis in validation studies : Uses and recommendations

Resumen tomado de la publicaci??n

Exploratory factor analysis of the Brazilian OHIP for edentulous subjects

P>The use of seven domains for the Oral Health Impact Profile (OHIP)-EDENT was not supported for its Brazilian version, making data interpretation in clinical settings difficult. Thus, the aim of this study was to assess patients` responses for the translated OHIP-EDENT in a group of edentulous subjects and to develop factor scales for application in future studies. Data from 103 conventional and implant-retained complete denture wearers (36 men, mean age of 69 center dot 1 +/- 10 center dot 3 years) were assessed using the Brazilian version of the OHIP-EDENT. Oral health-related quality of life domains were identified by factor analysis using principal component analysis as the extraction method, followed by varimax rotation. Factor analysis identified four factors that accounted for 63% of the 19 items total variance, named masticatory discomfort and disability (four items), psychological discomfort and disability (five items), social disability (five items) and oral pain and discomfort (five items). Four factors/domains of the Brazilian OHIP-EDENT version represent patient-important aspects of oral health-related quality of life.

Relationship between diet and anticoagulant response to warfarin - A factor analysis

Background Diet composition is one of the factors that may contribute to intraindividual variability in the anticoagulant response to warfarin. Aim of the study To determine the associations between food pattern and anticoagulant response to warfarin in a group of Brazilian patients with vascular disease. Methods Recent and usual food intakes were assessed in 115 patients receiving warfarin; and corresponding plasma phylloquinone (vitamin K-1), serum triglyceride concentrations, prothrombin time (PT), and International Normalized Ratio (INR) were determined. A factor analysis was used to examine the association of specific foods and biochemical variables with anticoagulant data. Results Mean age was 59 +/- 15 years. Inadequate anticoagulation, defined as values of INR 2 or 3, was found in 48% of the patients. Soybean oil and kidney beans were the primary food sources of phylloquinone intake. Factor analysis yielded four separate factors, explaining 56.4% of the total variance in the data set. The factor analysis revealed that intakes of kidney beans and soybean oil, 24-h recall of phylloquinone intake, PT and INR loaded significantly on factor 1. Triglycerides, PT, INR, plasma phylloquinone, and duration of anticoagulation therapy loaded on factor 3. Conclusion Fluctuations in phylloquinone intake, particularly from kidney beans, and plasma phylloquinone concentrations were associated with variation in measures of anticoagulation (PT and INR) in a Brazilian group of patients with vascular disease.

Metabolic profiling by ultra-performance liquid chromatography-mass spectrometry and parallel factor analysis for the determination of disease biomarkers in Eucalyptus

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Confirmatory factor analysis of different versions of the Body Shape Questionnaire applied to Brazilian university students

This study aimed at evaluating the validity, reliability, and factorial invariance of the complete (34-item) and shortened (8-item and 16-item) versions of the Body Shape Questionnaire (BSQ) when applied to Brazilian university students. A total of 739 female students with a mean age of 20.44 (standard deviation = 2.45) years participated. Confirmatory factor analysis was conducted to verify the degree to which the one-factor structure satisfies the proposal for the BSQ's expected structure. Two items of the 34-item version were excluded because they had factor weights (lambda)< 40. All models had adequate convergent validity (average variance extracted =.43-.58; composite reliability=.85-.97) and internal consistency (alpha =.85-.97). The 8-item B version was considered the best shortened BSQ version (Akaike information criterion = 84.07, Bayes information criterion = 157.75, Browne-Cudeck criterion= 84.46), with strong invariance for independent samples (Delta chi(2)lambda(7)= 5.06, Delta chi(2)Cov(8)= 5.11, Delta chi(2)Res(16) = 19.30). (C) 2014 Elsevier Ltd. All rights reserved.

The Use of Factor Analysis in the Development of Hand Sizes for Glove Design

Factor analysis was used to develop a more detailed description of the human hand to be used in the creation of glove sizes; currently gloves sizes are small, medium, and large. The created glove sizes provide glove designers with the ability to create a glove design that can provide fit to the majority of hand variations in both the male and female populations. The research used the American National Survey (ANSUR) data that was collected in 1988. This data contains eighty-six length, width, height, and circumference measurements of the human hand for one thousand male subjects and thirteen hundred female subjects. Eliminating redundant measurements reduced the data to forty-six essential measurements. Factor analysis grouped the variables to form three factors. The factors were used to generate hand sizes by using percentiles along each factor axis. Two different sizing systems were created. The first system contains 125 sizes for male and female. The second system contains 7 sizes for males and 14 sizes for females. The sizing systems were compared to another hand sizing system that was created using the ANSUR database indicating that the systems created using factor analysis provide better fit.

Risk Factor Analysis of Late Survival After Heart Transplantation According to Donor Profile: A Multi-Institutional Retrospective Study of 512 Transplants

Introduction. Patients with terminal heart failure have increased more than the available organs leading to a high mortality rate on the waiting list. Use of Marginal and expanded criteria donors has increased due to the heart shortage. Objective. We analyzed all heart transplantations (HTx) in Sao Paulo state over 8 years for donor profile and recipient risk factors. Method. This multi-institutional review collected HTx data from all institutions in the state of Sao Paulo, Brazil. From 2002 to 2008 (6 years), only 512 (28.8%) of 1777 available heart donors were accepted for transplantation. All medical records were analyzed retrospectively; none of the used donors was excluded, even those considered to be nonstandard. Results. The hospital mortality rate was 27.9% (n = 143) and the average follow-up time was 29.4 +/- 28.4 months. The survival rate was 55.5% (n = 285) at 6 years after HTx. Univariate analysis showed the following factors to impact survival: age (P = .0004), arterial hypertension (P = .4620), norepinephrine (P = .0450), cardiac arrest (P = .8500), diabetes mellitus (P = .5120), infection (P = .1470), CKMB (creatine kinase MB) (P = .8694), creatinine (P = .7225), and Na+ (P = .3273). On multivariate analysis, only age showed significance; logistic regression showed a significant cut-off at 40 years: organs from donors older than 40 years showed a lower late survival rates (P = .0032). Conclusions. Donor age older than 40 years represents an important risk factor for survival after HTx. Neither donor gender nor norepinephrine use negatively affected early survival.

Factor analysis of responses to thermal, electrical, and mechanical painful stimuli supports the importance of multi-modal pain assessment

During the last decade, a multi-modal approach has been established in human experimental pain research for assessing pain thresholds and responses to various experimental pain modalities. Studies have concluded that differences in responses to pain stimuli are mainly related to variation between individuals rather than variation in response to different stimulus modalities. In a factor analysis of 272 consecutive volunteers (137 men and 135 women) who underwent tests with different experimental pain modalities, it was determined whether responses to different pain modalities represent distinct individual uncorrelated dimensions of pain perception. Volunteers underwent single painful electrical stimulation, repeated painful electrical stimulation (temporal summation), test for reflex receptive field, pressure pain stimulation, heat pain stimulation, cold pain stimulation, and a cold pressor test (ice water test). Five distinct factors were found representing responses to 5 distinct experimental pain modalities: pressure, heat, cold, electrical stimulation, and reflex-receptive fields. Each of the factors explained approximately 8% to 35% of the observed variance, and the 5 factors cumulatively explained 94% of the variance. The correlation between the 5 factors was near null (median ρ=0.00, range -0.03 to 0.05), with 95% confidence intervals for pairwise correlations between 2 factors excluding any relevant correlation. Results were almost similar for analyses stratified according to gender and age. Responses to different experimental pain modalities represent different specific dimensions and should be assessed in combination in future pharmacological and clinical studies to represent the complexity of nociception and pain experience.