Estimation Of Various Parameters Research Articles

Principal components regression and r-k class predictions in linear mixed models

In this article, we propose the principal components regression and r-k class predictors, which combine the techniques of the ridge and principal components regressions in the linear mixed models. We demonstrate that the Henderson's predictors, the ridge predictors and the principal components regression predictors are special cases of the r-k class predictors. We also research assumption that the variance parameters are not known and get estimators of variance parameters. The necessary and sufficient conditions for the superiorities of the r-k class predictors over each of these three predictors are obtained by the criterion of mean square error matrix. Furthermore, we suggest tests to approve if these conditions are indeed satisfied. Finally, real data analysis and a simulation study are used to illustrate the findings.

Experimental evidence of a pathogen invasion threshold.

Host density thresholds to pathogen invasion separate regions of parameter space corresponding to endemic and disease-free states. The host density threshold is a central concept in theoretical epidemiology and a common target of human and wildlife disease control programmes, but there is mixed evidence supporting the existence of thresholds, especially in wildlife populations or for pathogens with complex transmission modes (e.g. environmental transmission). Here, we demonstrate the existence of a host density threshold for an environmentally transmitted pathogen by combining an epidemiological model with a microcosm experiment. Experimental epidemics consisted of replicate populations of naive crustacean zooplankton (Daphnia dentifera) hosts across a range of host densities (20–640 hosts l−1) that were exposed to an environmentally transmitted fungal pathogen (Metschnikowia bicuspidata). Epidemiological model simulations, parametrized independently of the experiment, qualitatively predicted experimental pathogen invasion thresholds. Variability in parameter estimates did not strongly influence outcomes, though systematic changes to key parameters have the potential to shift pathogen invasion thresholds. In summary, we provide one of the first clear experimental demonstrations of pathogen invasion thresholds in a replicated experimental system, and provide evidence that such thresholds may be predictable using independently constructed epidemiological models.

On intraclass structure estimation in the growth curve model

In this paper the growth curve model, with the data correlated according to uniform structure, is considered. It represents a useful statistical model for a variety of areas. Our aim is to present various estimators of unknown variance parameters and compare their statistical properties. In the first part the review of known results for different estimators of $$\rho $$ and $$\sigma ^2$$ and their properties is given. The aim is to compare and order these estimators based on biasedness and mean square error.

Identifying mechanisms of stance control: A single stimulus multiple output model-fit approach

BackgroundPosture control models are instrumental to interpret experimental data and test hypotheses. However, as models have increased in complexity to include multi-segmental dynamics, discrepancy has arisen amongst researchers regarding the accuracy and limitations of identifying neural control parameters using a single stimulus. New methodThe current study examines this topic using simulations with a parameterized model-fit approach. We first determine if the model-fit approach can identify parameters in the theoretical situation with no noise. Then, we measure variability and bias of parameter estimates when realistic noise is included. We also address how the accuracy is influenced by the frequency bandwidth of the stimulus, signal-to-noise of the data, and fitting procedures. ResultsWe found perfect identification of parameters in the theoretical model without noise. With realistic noise, bias errors were 4.4% and 7.6% for fits that included frequencies 0.02–1.2 Hz and 0.02–0.4 Hz, respectively. Fits between 0.02–1.2 Hz also had the lowest variability in parameter estimates compared to other bandwidths. Parameters with the lowest variability tended to have the largest influence on body sways. Results also demonstrated the importance of closely examining model fits because of limitations in fitting algorithms. Comparison with existing methodThe single-input model-fit approach may be a simpler and more practical method for identifying neural control mechanisms compared to a multi-stimulus alternative. ConclusionsThis study provides timely theoretical and practical considerations applicable to the design and analysis of experiments contributing to the identification of mechanisms underlying stance control of a multi-segment body.

Comparison of estimators of variance parameters in the growth curve model with a special variance structure

Three different estimators of the variance parameters in the growth curve model with generalized uniform correlation structure are compared on the basis of mean square error. Since the situation in general depends on specific choice of the structure matrix, we investigate two important special cases.

A new REML (parameter expanded) EM algorithm for linear mixed models

SummaryLinear mixed models are regularly applied to animal and plant breeding data to evaluate genetic potential. Residual maximum likelihood (REML) is the preferred method for estimating variance parameters associated with this type of model. Typically an iterative algorithm is required for the estimation of variance parameters. Two algorithms which can be used for this purpose are the expectation‐maximisation (EM) algorithm and the parameter expanded EM (PX‐EM) algorithm. Both, particularly the EM algorithm, can be slow to converge when compared to a Newton‐Raphson type scheme such as the average information (AI) algorithm. The EM and PX‐EM algorithms require specification of the complete data, including the incomplete and missing data. We consider a new incomplete data specification based on a conditional derivation of REML. We illustrate the use of the resulting new algorithm through two examples: a sire model for lamb weight data and a balanced incomplete block soybean variety trial. In the cases where the AI algorithm failed, a REML PX‐EM based on the new incomplete data specification converged in 28% to 30% fewer iterations than the alternative REML PX‐EM specification. For the soybean example a REML EM algorithm using the new specification converged in fewer iterations than the current standard specification of a REML PX‐EM algorithm. The new specification integrates linear mixed models, Henderson's mixed model equations, REML and the REML EM algorithm into a cohesive framework.

Comparison of social capital indicators from position generators and name generators in predicting activity selection

Existing research on social capital and activity behavior has generally used name generators to analyze core networks to understand more intimate connections. But using name generators and interpreters in surveys increase respondent burden and survey length. The position generator is a technique used in the social science to study social capital and allows for measuring access to networked resources via occupational diversity of network contacts. The influence of these social capital measures is mostly unknown in the context of activity and travel. Since few activity-travel studies have used the position generator previously, a case study using the Pew Internet Personal Networks and Community survey was performed to explore the role of social network occupational diversity in activity participation. The name generator and position generator indicators were compared for predicting activity participation. Social capital was correlated with activity participation for all of the activity types analyzed. Network diversity as measured from the position generator was found to be a reasonable predictive variable for activity participation. The network diversity indicator was found to hold more explanatory and predictive power than core network indicators from a name generator. Additionally, due to the limited use of position generators in travel behavior analysis, the robustness of the social network occupational diversity measure was analyzed. On the measures of predictive accuracy, model fit, and bias and variability of parameter estimates, social network occupational diversity was found to be robust to varying position generator lengths.

Do safety performance functions used for predicting crash frequency vary across space? Applying geographically weighted regressions to account for spatial heterogeneity

Safety Performance Functions (SPFs) provide a basis for identifying locations where countermeasures can be effective. While SPFs in the Highway Safety Manual (HSM) were calibrated based on data from select states, calibration factors can be developed to localize SPFs to other states. Calibration factors typically provide a coarse adjustment—time and space stationarity of associations between crash frequencies and various factors is still assumed, implying that the SPF functional form is transferable. However, with increasing availability of statewide geo-referenced safety data, new spatial analysis methods, and increasing computational power, it is possible to relax the stationarity assumption. Specifically, to address spatial heterogeneity in SPFs, this study proposes relaxing SPFs (referring to them as Localized SPFs (L-SPFs)) that can be developed by using sophisticated geo-spatial modeling techniques that allow correlates of crash frequencies to vary in space. For demonstration, a 2013 geo-referenced freeway crash and traffic database from Virginia is used. As a potential methodological alternative, crash frequencies are predicted by estimating Geographically Weighted Negative Binomial Regressions. This model significantly outperforms the traditional negative binomial model in terms of model goodness-of-fit, providing a better and fuller understanding of spatial variations in modeled relationships. Our study results uncover significant spatial variations in parameter estimates for Annual Average Daily Traffic (AADT) and segment length. Ignoring such variations can result in prediction errors. The results indicate low transferability of a single statewide SPF highlighting the importance of developing L-SPFs. From a practical standpoint, L-SPFs can better predict crash frequencies and support prioritizing safety improvements in specific locations.

Profile-likelihood Confidence Intervals in Item Response Theory Models

ABSTRACTConfidence intervals (CIs) are fundamental inferential devices which quantify the sampling variability of parameter estimates. In item response theory, CIs have been primarily obtained from large-sample Wald-type approaches based on standard error estimates, derived from the observed or expected information matrix, after parameters have been estimated via maximum likelihood. An alternative approach to constructing CIs is to quantify sampling variability directly from the likelihood function with a technique known as profile-likelihood confidence intervals (PL CIs). In this article, we introduce PL CIs for item response theory models, compare PL CIs to classical large-sample Wald-type CIs, and demonstrate important distinctions among these CIs. CIs are then constructed for parameters directly estimated in the specified model and for transformed parameters which are often obtained post-estimation. Monte Carlo simulation results suggest that PL CIs perform consistently better than Wald-type CIs for both non-transformed and transformed parameters.

Parameters estimation of correlated non‐Gaussian processes by the method of polynomial maximisation

This study is devoted to the development of the new methods and algorithms of the parameter estimation (PE) of correlated non-Gaussian processes. The modified method of polynomial maximisation and the new models of random processes in the form of higher-order statistics were used for syntheses of the polynomial algorithms. It is shown that the non-linear processing of samples, the moment and the cumulant description of correlated non-Gaussian processes, and taking into account their parameters such as the cumulant coefficients of the third and higher orders can decrease the variance of PE as compared with the well-known results.

Spatiotemporal Dynamics and Spatial Determinants of Urban Growth in Suzhou, China

This paper analyzes the spatiotemporal dynamics of urban growth and models its spatial determinants in China through a case study of Suzhou, a rapidly industrializing and globalizing city. We conducted spatial analysis on land use data derived from multi-temporal remote sensing images of Suzhou from 1986 to 2008. Three urban growth types, namely infilling, edge-expansion, and leapfrog, were identified. We used landscape metrics to quantify the temporal trend of urban growth in Suzhou. During these 22 years, Suzhou’s urbanization changed from bottom-up rural urbanization to city-based top-down urban expansion. The underlying mechanism changed from TVE (town village enterprise) driven rural industrialization to FDI (foreign direct investment) driven development zone fever. Furthermore, we employed both global and local logistic regressions to model the probability of urban land conversion against a set of spatial variables. The global logistic regression model found the significance of proximity, neighborhood conditions, and socioeconomic factors. The logistic geographically weighted regression (GWR) model improved the global regression model with better model goodness-of-fit and higher prediction accuracy. More importantly, the local parameter estimates of variables enabled us to exam spatial variations of the influences of variables on urban growth in Suzhou.

Data mining for state space orthogonalization in adaptive dynamic programming

Dynamic programming (DP) is a mathematical programming approach for optimizing a system that changes over time and is a common approach for developing intelligent systems. Expert systems that are intelligent must be able to adapt dynamically over time. An optimal DP policy identifies the optimal decision dependent on the current state of the system. Hence, the decisions controlling the system can intelligently adapt to changing system states. Although DP has existed since Bellman introduced it in 1957, exact DP policies are only possible for problems with low dimension or under very limiting restrictions. Fortunately, advances in computational power have given rise to approximate DP (ADP). However, most ADP algorithms are still computationally-intractable for high-dimensional problems. This paper specifically considers continuous-state DP problems in which the state variables are multicollinear. The issue of multicollinearity is currently ignored in the ADP literature, but in the statistics community it is well known that high multicollinearity leads to unstable (high variance) parameter estimates in statistical modeling. While not all real world DP applications involve high multicollinearity, it is not uncommon for real cases to involve observed state variables that are correlated, such as the air quality ozone pollution application studied in this research. Correlation is a common occurrence in observed data, including sources in meteorology, energy, finance, manufacturing, health care, etc.ADP algorithms for continuous-state DP achieve an approximate solution through discretization of the state space and model approximations. Typical state space discretizations involve full-dimensional grids or random sampling. The former option requires exponential growth in the number of state points as the state space dimension grows, while the latter option is typically inefficient and requires an intractable number of state points. The exception is computationally-tractable ADP methods based on a design and analysis of computer experiments (DACE) approach. However, the DACE approach utilizes ideal experimental designs that are (nearly) orthogonal, and a multicollinear state space will not be appropriately represented by such ideal experimental designs. While one could directly build approximations over the multicollinear state space, the issue of unstable model approximations remains unaddressed. Our approach for handling multicollinearity employs data mining methods for two purposes: (1) to reduce the dimensionality of a DP problem and (2) to orthogonalize a multicollinear DP state space and enable the use of a computationally-efficient DACE-based ADP approach. Our results demonstrate the risk of ignoring high multicollinearity, quantified by high variance inflation factors representing model instability. Our comparisons using an air quality ozone pollution case study provide guidance on combining feature selection and feature extraction to guarantee orthogonality while achieving over 95% dimension reduction and good model accuracy.

Robust Inference from Conditional Logistic Regression Applied to Movement and Habitat Selection Analysis.

Conditional logistic regression (CLR) is widely used to analyze habitat selection and movement of animals when resource availability changes over space and time. Observations used for these analyses are typically autocorrelated, which biases model-based variance estimation of CLR parameters. This bias can be corrected using generalized estimating equations (GEE), an approach that requires partitioning the data into independent clusters. Here we establish the link between clustering rules in GEE and their effectiveness to remove statistical biases in variance estimation of CLR parameters.The current lack of guidelines is such that broad variation in clustering rules can be found among studies (e.g., 14–450 clusters) with unknown consequences on the robustness of statistical inference. We simulated datasets reflecting conditions typical of field studies. Longitudinal data were generated based on several parameters of habitat selection with varying strength of autocorrelation and some individuals having more observations than others. We then evaluated how changing the number of clusters impacted the effectiveness of variance estimators. Simulations revealed that 30 clusters were sufficient to get unbiased and relatively precise estimates of variance of parameter estimates. The use of destructive sampling to increase the number of independent clusters was successful at removing statistical bias, but only when observations were temporally autocorrelated and the strength of inter-individual heterogeneity was weak. GEE also provided robust estimates of variance for different magnitudes of unbalanced datasets. Our simulations demonstrate that GEE should be estimated by assigning each individual to a cluster when at least 30 animals are followed, or by using destructive sampling for studies with fewer individuals having intermediate level of behavioural plasticity in selection and temporally autocorrelated observations. The simulations provide valuable information to build reliable habitat selection and movement models that allow for robustness of statistical inference without removing excessive amounts of ecological information.

Semiparametric fractional imputation using empirical likelihood in survey sampling

ABSTRACTThe empirical likelihood method is a powerful tool for incorporating moment conditions in statistical inference. We propose a novel application of the empirical likelihood for handling item non-response in survey sampling. The proposed method takes the form of fractional imputation but it does not require parametric model assumptions. Instead, only the first moment condition based on a regression model is assumed and the empirical likelihood method is applied to the observed residuals to get the fractional weights. The resulting semiparametric fractional imputation provides -consistent estimates for various parameters. Variance estimation is implemented using a jackknife method. Two limited simulation studies are presented to compare several imputation estimators.

Most Likely Separation of Intensity and Warping Effects in Image Registration

This paper introduces a class of mixed-effects models for joint modeling of spatially correlated intensity variation and warping variation in 2D images. Spatially correlated intensity variation and warp variation are modeled as random effects, resulting in a nonlinear mixed-effects model that enables simultaneous estimation of template and model parameters by optimization of the likelihood function. We propose an algorithm for fitting the model which alternates estimation of variance parameters and image registration. This approach avoids the potential estimation bias in the template estimate that arises when treating registration as a preprocessing step. We apply the model to datasets of facial images and 2D brain magnetic resonance images to illustrate the simultaneous estimation and prediction of intensity and warp effects.

How toxic is public debt?

This paper deals with the debt-growth relationship using several time-series tools. The idea is to find out whether the inverse relationship between these variables can be detected without imposing any functional forms on the estimating relationship and whether the relationship does indeed reflect some nonlinear features. Thus recursive correlations with different orderings of the time-series are computed using the Reinhart and Rogoff panel data. After that, recursive correlations are re-estimated with data that are cyclically adjusted to reflect the structural features of the two variables. The nature of the relationship is also scrutinised using several variable-parameter estimation techniques (Kalman filter, logistic functional form and recursive estimation). Finally, some causality analyses are carried out using various transformations of the data up to the point of cross-sections of data. The analysis shows that the inverse relationship between growth and debt is indeed quite robust and tends to support the 'toxic debt' hypothesis rather than the cyclical debt accumulation hypothesis. Yet the causality issue remains largely unresolved.

Bioinformatic processing of RAD‐seq data dramatically impacts downstream population genetic inference

Summary Restriction site‐associated DNA sequencing (RAD‐seq) provides high‐resolution population genomic data at low cost, and has become an important component in ecological and evolutionary studies. As with all high‐throughput technologies, analytic strategies require critical validation to ensure precise and unbiased interpretation. To test the impact of bioinformatic data processing on downstream population genetic inferences, we analysed mammalian RAD‐seq data (>100 individuals) with 312 combinations of methodology (de novo vs. mapping to references of increasing divergence) and filtering criteria (missing data, HWE, FIS, coverage, mapping and genotype quality). In an effort to identify commonalities and biases in all pipelines, we computed summary statistics (nr. loci, nr. SNP, π, Hetobs, FIS, FST, Ne and m) and compared the results to independent null expectations (isolation‐by‐distance correlation, expected transition‐to‐transversion ratio Ts/Tv and Mendelian mismatch rates of known parent–offspring trios). We observed large differences between reference‐based and de novo approaches, the former generally calling more SNPs and reducing FIS and Ts/Tv. Data completion levels showed little impact on most summary statistics, and FST estimates were robust across all pipelines. The site frequency spectrum was highly sensitive to the chosen approach as reflected in large variance of parameter estimates across demographic scenarios (single‐population bottlenecks and isolation‐with‐migration model). Null expectations were best met by reference‐based approaches, although contingent on the specific criteria. We recommend that RAD‐seq studies employ reference‐based approaches to a closely related genome, and due to the high stochasticity associated with the pipeline advocate the use of multiple pipelines to ensure robust population genetic and demographic inferences.

Regional Reproducibility of BOLD Calibration Parameter M, OEF and Resting-State CMRO2 Measurements with QUO2 MRI.

The current generation of calibrated MRI methods goes beyond simple localization of task-related responses to allow the mapping of resting-state cerebral metabolic rate of oxygen (CMRO2) in micromolar units and estimation of oxygen extraction fraction (OEF). Prior to the adoption of such techniques in neuroscience research applications, knowledge about the precision and accuracy of absolute estimates of CMRO2 and OEF is crucial and remains unexplored to this day. In this study, we addressed the question of methodological precision by assessing the regional inter-subject variance and intra-subject reproducibility of the BOLD calibration parameter M, OEF, O2 delivery and absolute CMRO2 estimates derived from a state-of-the-art calibrated BOLD technique, the QUantitative O2 (QUO2) approach. We acquired simultaneous measurements of CBF and R2* at rest and during periods of hypercapnia (HC) and hyperoxia (HO) on two separate scan sessions within 24 hours using a clinical 3 T MRI scanner. Maps of M, OEF, oxygen delivery and CMRO2, were estimated from the measured end-tidal O2, CBF0, CBFHC/HO and R2*HC/HO. Variability was assessed by computing the between-subject coefficients of variation (bwCV) and within-subject CV (wsCV) in seven ROIs. All tests GM-averaged values of CBF0, M, OEF, O2 delivery and CMRO2 were: 49.5 ± 6.4 mL/100 g/min, 4.69 ± 0.91%, 0.37 ± 0.06, 377 ± 51 μmol/100 g/min and 143 ± 34 μmol/100 g/min respectively. The variability of parameter estimates was found to be the lowest when averaged throughout all GM, with general trends toward higher CVs when averaged over smaller regions. Among the MRI measurements, the most reproducible across scans was R2*0 (wsCVGM = 0.33%) along with CBF0 (wsCVGM = 3.88%) and R2*HC (wsCVGM = 6.7%). CBFHC and R2*HO were found to have a higher intra-subject variability (wsCVGM = 22.4% and wsCVGM = 16% respectively), which is likely due to propagation of random measurement errors, especially for CBFHC due to the low contrast-to-noise ratio intrinsic to ASL. Reproducibility of the QUO2 derived estimates were computed, yielding a GM intra-subject reproducibility of 3.87% for O2 delivery, 16.8% for the M value, 13.6% for OEF and 15.2% for CMRO2. Although these results focus on the precision of the QUO2 method, rather than the accuracy, the information will be useful for calculation of statistical power in future validation studies and ultimately for research applications of the method. The higher test-retest variability for the more extensively modeled parameters (M, OEF, and CMRO2) highlights the need for further improvement of acquisition methods to reduce noise levels.

Estimates of Genetic Variance Parameters and General and Specific Combining Ability of Morphological Traits, Yield and Yield Components of Maize Hybrids in Normal and Salt Stress Conditions

Estimates of Genetic Variance Parameters and General and Specific Combining Ability of Morphological Traits, Yield and Yield Components of Maize Hybrids in Normal and Salt Stress Conditions

Big Data Smoothing and Outlier Removal for Patent Big Data Analysis

In general statistical analysis, we need to make a normal assumption. If this assumption is not satisfied, we cannot expect a good result of statistical data analysis. Most of statistical methods processing the outlier and noise also need to the assumption. But the assumption is not satisfied in big data because of its large volume and heterogeneity. So we propose a methodology based on box-plot and data smoothing for controling outlier and noise in big data analysis. The proposed methodology is not dependent upon the normal assumption. In addition, we select patent documents as target domain of big data because patent big data analysis is a important issue in management of technology. We analyze patent documents using big data learning methods for technology analysis. The collected patent data from patent databases on the world are preprocessed and analyzed by text mining and statistics. But the most researches about patent big data analysis did not consider the outlier and noise problem. This problem decreases the accuracy of prediction and increases the variance of parameter estimation. In this paper, we check the existence of the outlier and noise in patent big data. To know whether the outlier is or not in the patent big data, we use box-plot and smoothing visualization. We use the patent documents related to three dimensional printing technology to illustrate how the proposed methodology can be used for finding the existence of noise in the searched patent big data.