Violation of the sphericity assumption and its effect on Type-I error rates in repeated measures ANOVA and multi-level linear models (MLM)

This study aims to investigate the effects of violations of the sphericity assumption on Type I error rates for different methodical approaches of repeated measures analysis using a simulation approach. In contrast to previous simulation studies on this topic, up to nine measurement occasions were considered. Therefore, two populations representing the conditions of a violation vs. a non-violation of the sphericity assumption without any between-group effect or within-subject effect were created and 5,000 random samples of each population were drawn. Finally, the mean Type I error rates for Multilevel linear models (MLM) with an unstructured covariance matrix (MLM-UN), MLM with compound-symmetry (MLM-CS) and for repeated measures analysis of variance (rANOVA) models (without correction, with Greenhouse-Geisser-correction, and Huynh-Feldt-correction) were computed. To examine the effect of both the sample size and the number of measurement occasions, sample sizes of n = 20, 40, 60, 80, and 100 were considered as well as measurement occasions of m = 3, 6 and 9. For MLM-UN, the results illustrate a massive progressive bias for small sample sizes (n =20) and m = 6 or more measurement occasions. This effect could not be found in previous simulation studies with a smaller number of measurement occasions. The mean Type I error rates for rANOVA with Greenhouse-Geisser-correction demonstrate a small conservative bias if sphericity was not violated, sample sizes were small (n = 20), and m = 6 or more measurement occasions were conducted. The results plead for a use of rANOVA with Huynh-Feldt-correction, especially when the sphericity assumption is violated, the sample size is rather small and the number of measurement occasions is large. MLM-UN may be used when the sphericity assumption is violated and when sample sizes are large.Comment: 14 pages, 6 figure

Hierarchies of factor solutions in the intelligence domain : applying methodology from personality psychology to gain insights into the nature of intelligence

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Indeterminacy of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models

Two methods to calculate a measure for the quality of factor score estimates have been proposed. These methods were compared by means of a simulation study. The method based on a covariance matrix reproduced from a model leads to smaller effects of sampling error

Varimax rotation based on gradient projection needs between 10 and more than 500 random start loading matrices for optimal performance

Gradient projection rotation (GPR) is a promising method to rotate factor or component loadings by different criteria. Since the conditions for optimal performance of GPR-Varimax are widely unknown, this simulation study investigates GPR towards the Varimax criterion in principal component analysis. The conditions of the simulation study comprise two sample sizes (n = 100, n = 300), with orthogonal simple structure population models based on four numbers of components (3, 6, 9, 12), with- and without Kaiser-normalization, and six numbers of random start loading matrices for GPR-Varimax rotation (1, 10, 50, 100, 500, 1,000). GPR-Varimax rotation always performed better when at least 10 random matrices were used for start loadings instead of the identity matrix. GPR-Varimax worked better for a small number of components, larger (n = 300) as compared to smaller (n = 100) samples, and when loadings were Kaiser-normalized before rotation. To ensure optimal (stationary) performance of GPR-Varimax in recovering orthogonal simple structure, we recommend using at least 10 iterations of start loading matrices for the rotation of up to three components and 50 iterations for up to six components. For up to nine components, rotation should be based on a sample size of at least 300 cases, Kaiser-normalization, and more than 50 different start loading matrices. For more than nine components, GPR-Varimax rotation should be based on at least 300 cases, Kaiser-normalization, and at least 500 different start loading matrices.Comment: 19 pages, 8 figures, 2 tables, 4 figures in the Supplemen

Heat flux measurement from thermal infrared imagery in low-flux fumarolic zones: Example of the Ty fault (La Soufrière de Guadeloupe)

International audienceMonitoring the geothermal flux of a dormant volcano is necessary both for hazard assessment and for studying hydrothermal systems. Heat from a magma body located at depth is transported by steam to the surface, where it is expelled in fumaroles if the heat flow exceeds 500 W/m2. If the heat flow is lower than 500 W/m2, steam mainly condensates in the soil close to surface and produces a thermal anomaly detectable at the surface. In this study, we propose a method to quantify low heat fluxes from temperature anomalies measured at the surface by a thermal infrared camera. Once corrected from the atmospheric and surface effects, thermal infrared images are used to compute (1) the excess of radiative flux, (2) the excess of sensible flux and (3) the steam flux from the soil to the atmosphere. These calculations require measurements of atmospheric parameters (temperature, wind velocity and humidity) and estimations of surface parameters (roughness and emissivity). This method has been tested on a low-flux fumarolic zone of the Soufrière volcano (Guadeloupe Island -- Lesser Antilles), and compared to a flux estimation realized from the thermal gradient measurements into the soil. The two methods show a good agreement and a similar precision (267 ± 46 W/m2 for the thermal infrared method, and 275 ± 50 W/m2 for the vertical temperature gradient method), if surface roughness is well calibrated

Evidence for a new shallow magma intrusion at La Soufrière of Guadeloupe (Lesser Antilles). Insights from long-term geochemical monitoring of halogen- rich hydrothermal fluids

International audienceMore than three decades of geochemical monitoring of hot springs and fumaroles of La Soufrière of Guadeloupe allows the construction of a working model of the shallow hydrothermal system. This system is delimited by the nested caldera structures inherited from the repeated flank collapse events and the present dome built during the last magmatic eruption (1530 AD) and which has been highly fractured by the subsequent phreatic or phreatomagmatic eruptions. Because it is confined into the low volume, highly compartmented and partially sealed upper edifice structure, the hydrothermal system is highly reactive to perturbations in the volcanic activity (input of deep magmatic fluids), the edifice structure (sealing and fracturing) and meteorology (wet tropical regime). The current unrest, which began with a mild reactivation of fumarolic activity in 1990, increased markedly in 1992 with seismic swarms and an increase of degassing from the summit of the dome. In 1997 seismic activity increased further and was accompanied by a sudden high-flux HCl-rich gas from summit fumaroles. We focus on the interpretation of the time-series of the chemistry and temperature of fumarolic gases and hot springs as well as the relative behaviours of halogens (F, Cl, Br and I). This extensive geochemical time-series shows that the deep magmatic fluids have undergone large changes in composition due to condensation and chemical interaction with shallow groundwater (scrubbing). It is possible to trace back these processes and the potential contribution of a deep magmatic source using a limited set of geochemical time series: T, CO2 and total S content in fumaroles, T and Cl- in hot springs and the relative fractionations between F, Cl, Br and I in both fluids. Coupling 35 years of geochemical data with meteorological rainfall data and models of ion transport in the hydrothermal aquifers has allowed us to identify a series of magmatic gas pulses into the hydrothermal system since the 1976-1977 crisis. The contrasting behaviours of S- and Cl- bearing species in fumarolic gas and in thermal springs suggests that the current activity is the result of a new magma intrusion which was progressively emplaced at shallow depth since ~1992. Although it might still be evolving, the characteristics of this new intrusion indicate that it hasalready reached a magnitude similar to the intrusion that was emplaced during the 1976-1977 eruptive crisis. The assessment of potential hazards associated with evolution of the current unrest must consider the implications of recurrent intrusion and further pressurization of the hydrothermal system on the likelihood of renewed phreatic explosive activity. Moreover, the role of hydrothermal pressurization on the basal friction along low-strength layers within the upper part of the edifice must be evaluated with regards to partial flank collapse. At this stage enhanced monitoring, research, and data analysis is required to quantify the uncertainties related to future scenarios of renewed eruptive activity and magmatic evolution

A Schmid-Leiman-Based Transformation Resulting in Perfect Inter-correlations of Three Types of Factor Score Predictors

Factor score predictors are computed when individual factor scores are of interest. Conditions for a perfect inter-correlation of the best linear factor score predictor, the best linear conditionally unbiased predictor, and the determinant best linear correlation-preserving predictor are presented. A transformation resulting in perfect correlations of the three predictors is proposed

Steam and gas emission rates from La Soufrière of Guadeloupe (Antilles arc): implications for the magmatic supply degassing during unrest

Since its last magmatic eruption in 1530 AD, La Soufrière andesitic volcano in Guadeloupe has displayed intense hydrothermal activity and six phreatic eruptive crises (the last of which, in 1976-1977, with 73000 evacuees). Here we report on the first direct quantification of gas plume emissions from La Soufrière summit vents, which gradually intensified during the past 20 years. Gas fluxes were determined in 2006 then 2012 [1] by measuring the horizontal and vertical distribution of volcanic gas concentrations in the air-diluted plume, the composition of the hot fumarolic fluid at exit (108°C), and scaling to the speed of plume transport (in situ measurements and FLIR imaging). We first demonstrate that all fumarolic vents of La Soufrière are fed by a common H2O-rich (97-98 mol %) fluid end-member, emitted almost unmodified at the most active South Crater while affected by secondary alterations (steam condensation, sulphur scrubbing) at other vents. Daily fluxes in 2012 (200 tons of H2O, 15 tons of CO2, ~4 tons of H2S and 1 ton of HCl) were augmented by a factor ~3 compared to 2006, in agreement with increasing activity. Summit fumarolic degassing contributes most of the bulk volatile and heat budget (8 MW) of the volcano. Isotopic evidences demonstrate that La Soufrière hydrothermal emissions are sustained by continuous heat and gas supply from an andesitic magma reservoir confined at 6-7 km depth. This magmatic supply mixes with abundant groundwater of tropical meteoric origin in the hydrothermal system. Based on petro-geochemical data for the erupted magma(s), we assess that the volcanic gas fluxes in 2012 can be accounted for by the release of free magmatic gas derived from about 1000 m3 per day of the basaltic melt replenishing the reservoir at depth. In terms of mass budget, the current degassing unrest is compatible with enhanced free gas release from that reservoir, without requiring any (actually undetected) magma intrusion. We recommend a regular survey of the fumarolic gas flux from La Soufrière in order to anticipate the evolution of the magma reservoir. [1] P. Allard et al., Chemical Geology 384, 76-93, 2014