The Effects of Sampling Error and Model Characteristics on Parameter Estimation for Maximum Likelihood Confirmatory Factor Analysis.

A large-scale simulation design was used to study the sensitivity of maximum likelihood (ML) factor analysis to violations of measurement scale and distributional assumptions in the input data. Product-moment, polychoric. Spearman's rho, and Kendall's tau- b correlations computed from ordinal data were used to estimate a single-factor model. The resulting ML estimates were compared on the bases of convergence rates and improper solutions, accuracy of the loading estimates, fit statistics, and estimated standard errors. The LISREL maximum likelihood solution algorithm was used to estimate model parameters. The polychoric correlation procedure was found to provide the most accurate estimates of pairwise correlations and factor loadings but performed worst on all goodness-of-fit criteria. LISREL overestimated all standard errors, thus not reflecting the effects of standardization as previously assumed. When the data were categorized, the polychoric correlations led to the best estimates of the standard errors.

The interplay of the following factors: population design (PDN), the cost function in terms of maximum cost (Max. C) (i.e., maximum number of samples/sample size), sample size, and intersubject variability [restricted (30%) to moderate (60%)] on the estimation of pharmacokinetic parameters from population pharmacokinetic data sets obtained using mixed designs was investigated in a simulation study. A two compartment model with multiple bolus intravenous inputs was assumed, and the residual variability was set at 15%. The sample size (N) investigated ranged from 30 to 200 with the associated cost function varying accordingly with the five individual and sixteen population designs studied. Accurate and precise estimates of structural model parameters were obtained for N > or = 50 (Max. C > or = 150) irrespective of the intersubject variability (ITV) and PDN investigated. When ITV was 30%, all structural model parameters were well estimated irrespective of the PDN. Robust estimates of clearance and its variability were obtained for all N at all levels of ITV with Max. C > or = 90 (PDN > or = 4). Imprecise estimates of ITV in V1, V2, and Q were obtained at 60% ITV irrespective of N, PDN, or Max. C. Positive bias was associated with the estimation of variability in V1, V2, and Q with PDN < or = 4 (Max. C < or = 150). This was due in part to a greater proportion of subjects sampled only once. Correspondingly, residual variability was underestimated. It is of utmost importance to avoid this artifact by ensuring that at least a moderate subset of subjects contributing data to a population pharmacokinetic study contribute data more than once. Given a sample size and ITV, the cost function must be considered in designing a population pharmacokinetic study using mixed designs.

Hypothesis tests

In the present paper a mixed approach is proposed for the simultaneously estimation of regression and correlation structure parameters in multivariate probit models using generalized estimating equations for the former and pseudo-score equations for the latter. The finite sample properties of the corresponding estimators are compared to estimators proposed by Qu, Williams, Beck and Medendorp (1992) and Qu, Piedmonte and Williams (1994) using generalized estimating equations for both sets of parameters via a Monte Carlo experiment. As a `reference' estimator for an equicorrelation model, the maximum likelihood (ML) estimator of the random effects probit model is calculated. The results show the mixed approach to be the most robust approach in the sense that the number of datasets for which the corresponding estimates converged was largest relative to the other two approaches. Furthermore, the mixed approach led to the most efficient non-ML estimators and to very efficient estimators for regression and correlation structure parameters relative to the ML estimator if individual covariance matrices were used.

Commentary

Regarded as a marked category of global forests, forest plantations not only have great significance for the development of the global economy, but also contribute ecological and social benefits. The accurate acquisition of the multi-scale (from individual tree to landscape level) and near-real-time information of structural parameters in plantations is the premise of decision-making in sustainable management for the whole forest farm, and it is also the basis for the evaluation of forest productivity in stands. The development and synergetic applications of multi-source and multi-platform remote sensing technology provide a technical basis for the highly accurate estimation of multi-scale forest structural parameters. In this study, we developed an advanced framework for estimating these parameters of forest plantations in multiple scales (individual tree, plot and landscape levels) based on the Unmanned Aircraft System Light Detection and Ranging (UAS-LiDAR) transects and wall-to-wall Sentinel-2 imagery, combined with the sample plot data in a typical forest farm plantation (mainly Larch, Chinese pine) of Northern China. The position and height of individual trees within the plots were extracted by the LiDAR-based point cloud segmentation (PCS) algorithm, and then different approaches to the extrapolation of forest structural parameters from the plot to landscape level were assessed. The results demonstrate that, firstly, the individual tree height obtained by PCS was of relatively high accuracy (rRMSE = 1.5–3.3%); secondly, the accuracy of the forest structure parameters of the sample plot scale estimated by UAS-LiDAR is rRMSE = 4.4–10.6%; and thirdly, the accuracy of the two-stage upscaling approach by UAS-LiDAR transects as an intermediate stage (rRMSE = 14.5–20.2%) performed better than the direct usage of Sentinel-2 data (rRMSE = 22.9–27.3%). This study demonstrated an advanced framework for creating datasets of multi-scale forest structural parameters in a forest plantation, and proved that the synergetic usage of UAS-LiDAR transects and full coverage medium-resolution satellite imagery can provide a high-precision and low-cost technical basis for the multi-level estimation of forest structural parameters.

This study investigates item parameter recovery, standard error estimates, and fit statistics yielded by the WINSTEPS program under the Rasch model and the rating scale model through Monte Carlo simulations. The independent variables were item response model, test length, and sample size. WINSTEPS yielded practically unbiased estimates for the difficulty parameters under the Rasch model and the overall difficulty parameters under the rating scale model. However, the estimates for the intersection parameters under the rating scale model were substantially biased, especially for short tests. The standard errors of the overall difficulties and intersection parameters were slightly underestimated. The cube root-transformed weighted and unweighted item fit statistics did not follow the standard normal distribution in that their empirical sampling variances were much smaller than the expected value of unity. Correction procedures were proposed to make them follow approximately the standard normal distribution so that the usual critical ranges at the α nominal level could be used to screen the misfitting items.

A new time-domain method is suggested in this paper for simultaneous identification of the structural parameters and the time history of the input excitation using output-only measurements. The proposed method is based on an iterative identification procedure consisting of the least-squares identification technique and a modification process between each iterative step. The modification process is introduced to convert the spatial information of the external excitation into mathematical conditions. First, the unknown force vector is conjectured through the equation of motion using the initial guess of the structural parameters and the measured structural responses. The estimated input force vector is then modified to force it comply with the spatial distribution of the external excitations. The modified input force vector is further used to provide new estimation of structural parameters. Repeat the aforementioned procedure until the structural parameters satisfy the preset convergence criterion. Numerical examples as shear building and truss bridge model are employed to evaluate the feasibility of the proposed method. In the numerical examples, typical scenario of complete and noise-free as well as incomplete and noise-contaminated output measurements are considered. The results demonstrate that the proposed method can accurately identify both the structural parameters and the input time history for the cases that the structural responses are not polluted or slightly contaminated by measurement noise.

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large sample x2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.

Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials

SummaryThis paper proposes a method to identify the time‐variant modal frequencies of high‐rise buildings and applies the method to the field measurements from a 68‐story high‐rise building during Super Typhoon Mangkhut (September 16, 2018). The analyzed results show that the fundamental natural frequencies of the monitored building first gradually decreased by about 9% and then returned to 94% of the original values over time. Moreover, the effects of time‐variant modal frequencies on damping estimation of high‐rise buildings are investigated by a comprehensive parametric study. The results indicate that the change rate of frequency has significant effects on the damping estimation by the conventional modal identification methods such as the random decrement technique and Bayesian spectral density approach. Accordingly, an error model for describing the relationship between the estimation error of damping ratio and main parameters of time‐variant modal frequencies is established. Then, an error model‐based correction method is proposed for the conventional damping identification methods to eliminate the estimation errors of damping ratios due to the time‐variant modal frequencies, which is proved to be effective through Monte Carlo simulation and is further applied to identify the time‐variant damping ratios of the monitored high‐rise building. This paper aims to further the understanding of structural dynamic properties of high‐rise buildings during typhoons and provide accurate estimation of structural modal parameters.

The four dimensions of sensation seeking: a confirmatory factor analysis

A confirmatory factor analysis of the WMS-III in a clinical sample with crossvalidation in the standardization sample

This new method of identifying structural parameters, called 'symbolization-based differential evolution strategy' (SDES), merges the advantages of symbolic time series analysis and differential evolution (DE). Data symbolization in SDES alleviates the effects of harmful noise. SDES was numerically compared with particle swarm optimization and DE on raw acceleration data. These simulations revealed that SDES provided better estimates of structural parameters when the data were contaminated by noise. We applied SDES to experimental data to assess its feasibility in realistic problems. SDES performed much better than particle swarm optimization and DE on raw acceleration data. The simulations and experiments show that SDES is a powerful tool for identifying unknown parameters of structural systems even when the data are contaminated with relatively large amounts of noise. Copyright © 2012 John Wiley & Sons, Ltd.

Sufficient statistics for unobserved heterogeneity in structural dynamic logit models