Anders Christoffersson

Factor analysis of dichotomized variables

An approach for multiple factor analysis of dichotomized variables is presented. It is based on the distribution of the first and second order joint probabilities of the binary scored items. The estimator is based on the generalized least squares principle. Standard errors and a test of the fit of the model is given.

Simultaneous factor analysis of dichotomous variables in several groups

A new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals. The method makes it possible to compare factor loading pattern, factor variances and covariances, and factor means over groups. The method uses information from first and second order proportions and estimates the model by generalized least-squares. Hypotheses regarding different degrees of invariance over groups may be evaluated by a large-sample chi-square test.

Tomographical mapping of the lithosphere and asthenosphere beneath southern Scandinavia and adjacent areas

Abstract In this paper we report on a seismic tomographical survey of the lithosphere-asthenosphere beneath southern Scandinavia and adjacent areas. The ACH-inversion technique has been used, and the observational data in the form of P-wave travel-time residuals have been obtained from seismogram records from networks in Denmark, southern Norway and southern Sweden. The volume under investigation, subdivided into four levels (layers) of 7 × 7 knots (blocks) each for estimation of velocity perturbations, covers the area 54°–62°N and 7°–20°E and depth range 0–600 km. Major findings are as follows. Level 1 (0–100 km): pronounced velocity lows beneath southern Jutland, Zealand (the Variscan Foredeep) and the Sveco-Norwegian province of southeastern Norway (1500 Ma old). The Svecofennides of southeastern Sweden exhibit relatively high velocities, while the Sveco-Norwegian province of southwestern Sweden (1700 Ma old) is characterized by moderately high velocities. The transition between velocity highs and lows coincides with the Tornquist-Teisseyre Line (TTL) (or Fennoscundian Border Zone). Level 2 (100–300 km): velocity anomalies are less pronounced at this level, although velocity lows are found beneath the northern Jutland-Zealand area and slightly northwestwards of the Oslo Rift. The only velocity high is found beneath the southeasternmost part of Sweden. The TTL does not appear to have a clear counterpart in the velocity anomaly pattern in this depth range, although a clearly unambiguous answer here would require far more extensive observational data—a research goal of the future. Level 3 (300–500 km) and Level 4 (500–600 km): velocity anomalies are weak, which is not unexpected for the upper mantle beneath shield areas.

Two-step weighted least squares factor analysis of dichotomized variables

A two-step weighted least squares estimator for multiple factor analysis of dichotomized variables is discussed. The estimator is based on the first and second order joint probabilities. Asymptotic standard errors and a model test are obtained by applying the Jackknife procedure.

Statistical Models for Seismic Magnitude

Abstract In this paper some statistical models in connection with seismic magnitude are presented. Two main situations are treated. The first deals with the estimation of magnitude for an event, using a fixed network of stations and taking into account the detection and bias properties of the individual stations. The second treats the problem of estimating seismicity, and detection and bias properties of individual stations. The models are applied to analyze the magnitude bias effects for an earthquake aftershock sequence from Japan, as recorded by a hypothetical network of 15 stations. It is found that network magnitudes computed by the conventional averaging technique are considerably biased, and that a maximum likelihood approach using instantaneous noise-level estimates for non-detecting stations gives the most consistent magnitude estimates. Finally, the models are applied to evaluate the detection characteristics and associated seismicity as recorded by three VELA arrays: UBO (Uinta Basin), TFO (Tonto Forest) and WMO (Wichita Mountains).

A short note on the estimation of the asymptotic covariance matrix for polychoric correlations

By using a Taylor expansion of the equations that define the two step estimator for polychoric correlations, the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way.

Model Based Frequency Domain Estimation of the Thermal Properties of Building Insulation

Estimation of the thermal resistance (R) and (especially) the thermal capacity (C) of building components from in situ measurements involves the analy sis of dynamic (not steady-state) heat flow data. Such analyses require a suitable dynamic model of the system. Such models, and thus analyses, are most elegantly handled in the frequency domain. Such modeling shows that in realistic experimental situations the presence of the heat flux transducer can have a significant effect on the dynamics of the system, even if the R and C of the transducer are much smaller than those of the component. This is confirmed by analysis of a real data set. Inclusion of the transducer in our model of the system produces estimates which, especially for short and highly dynamic data series, are more accurate and robust than those pro duced using more traditional time domain techniques.

Asymptotic efficiency of the pseudo‐maximum likelihood estimator in multi‐group factor models with pooled data

A multi-group factor model is suitable for data originating from different strata. However, it often requires a relatively large sample size to avoid numerical issues such as non-convergence and non-positive definite covariance matrices. An alternative is to pool data from different groups in which a single-group factor model is fitted to the pooled data using maximum likelihood. In this paper, properties of pseudo-maximum likelihood (PML) estimators for pooled data are studied. The pooled data are assumed to be normally distributed from a single group. The resulting asymptotic efficiency of the PML estimators of factor loadings is compared with that of the multi-group maximum likelihood estimators. The effect of pooling is investigated through a two-group factor model. The variances of factor loadings for the pooled data are underestimated under the normal theory when error variances in the smaller group are larger. Underestimation is due to dependence between the pooled factors and pooled error terms. Small-sample properties of the PML estimators are also investigated using a Monte Carlo study.

Trinity or Verity

Single-station three-component analysis is applied to seismic recordings in Norway from quarry blasts on the Kola peninsula. Even for P-waves, non-linear particle motions are observed, implying phase shifts between the horizontal and vertical components. Such instantaneous phase-lags provide direct and useful information on the arrival of different wave types, and this is illustrated. For P-waves, the most probable origin of these phase shifts is scattering and P-to-S conversion. Phase-lags are also observed for later phases. Using signal particle motion models which allow for phase shifts we have been successful in analysing several different phases (P, S and Lg) in these complex regional events. Such results contrast with various previous studies of this and similar data, in which three-component analysis was found to be relatively ineffective. We attribute this significant difference in results in part to sub-optimal processing parameters and/or three-component analysis methods in some of the earlier studies e.g. analysis based on visual inspection of particle motion figures (very difficult where phase-lags are involved) or on eigenvector analysis where the diagonal elements of the covariance matrix, and thus uncorrelated noise, have a large influence. Incorporating seismic wavefield physics leads to signal models which can be expressed primarily in terms of off-diagonal elements and such models are therefore inherently more robust.

Optimum Approaches to Magnitude Measurements

Conventional magnitude estimates from a seismic network are based on measurements from only those stations which actually detect a given event, thus ignoring the data from stations where the signal amplitude is below the detection threshold. The topic of this paper is to review some recent developments in magnitude estimation methods, using information from both detecting and non-detecting stations, and it is shown that this leads to significant improvments in magnitude estimates for small events. The method is applied to study the linearity of the mb:Ms relation of earthquakes, and it is found that the apparent curvature of observed mb:Ms relationships can be explained through detectability considerations alone. Thus, from the available data, there is no need to assume a change of the mb:Ms slope at low magnitudes. Finally, the method is used to obtain a separation curve between earthquakes and explosions on the mb:Ms diagram which represents an improvement compared to conventional approaches.