Linear Static Models with Additive Effects

Many researchers have studied the relationships among heterogeneous foreign direct investment (FDI), environmental regulation, and green total factor productivity. However, no research has been done on how different types of FDI can result in green technology spillover under different levels of environmental regulation intensity. To address this research gap, in this paper, we build a static linear panel model, a static panel threshold model, and a dynamic panel threshold model to investigate the environmental regulatory threshold effect of labor-based FDI and capital-based FDI in terms of their green technology spillover. Based on the measurement of green total factor productivity (GTFP) of 36 industry sectors in China from 2003 to 2015, we first compare the threshold effects of environmental regulation on green technology spillover between labor-based FDI and capital-based FDI with a static linear model and a static threshold model. The results show that environmental regulation is unable to significantly promote the green technology spillover of labor-based FDI. However, intensifying environmental regulation can reduce the negative impact of labor-based FDI on GTFP. The effect of environmental regulation on green technology spillover of capital-based FDI is more complex. In the static linear model, environmental regulation can significantly promote the green technology spillover of capital-based FDI. In the static threshold model, the green technology spillover of capital-based FDI exists only when the environmental regulation intensity is sufficiently low or sufficiently high. Finally, the dynamic threshold model is adopted for robustness check. The results show when the environmental regulation intensity is higher than a threshold, both types of FDI can indeed result in green technology spillover. In short, our results prove that to ensure that FDI results in green technology spillover, it is necessary to continue to strengthen environmental regulation.

Ogle proposed two measures of oculomotor balance, called associated and disassociated phorias, which he assumed were equivalent. However, experimentally determined values of these phorias do not show a close correspondence. To analyze the rationale behind Ogle's assumption of equality, a linear static model was evaluated. It was found that indeed the linear model predicts an exact correspondence between associated and disassociated phorias. Thus, his assumption depended on the presence of a linear model. To account for the discrepancy between these two measures, a nonlinear static model, containing the dead space operators depth of field and Panum's fusional area, was evaluated. Four equations for fixation disparity were derived corresponding to the four combinations of deadspace operator outputs. It was found that only one of these four equally possible solutions for associated phoria corresponded to the disassociated phoria. This suggests that the variability in the four solutions may account for the scatter in the experimental data. The nonlinear model was analyzed further to determine its sensitivity to parameter changes and to show how such a model could generate the classical shape of the fixation disparity curve.

Ogle and his colleagues proposed two measures of oculomotor linkage called the accommodative convergence to accommodation (AC/A) ratio. This ratio provided a clinically useful assessment of the drive of accommodation, or focusing system, on vergence, or binocular fixation system. The phoria method measured the relatively large deviation in eye alignment under the monocular condition, whereas the fixation disparity method measured the relatively small misalignment of the eyes under the binocular condition to obtain the AC/A ratio. Ogle et al. indicated that these two measures should be equal. However, experimental results showed a substantial difference between the AC/A ratios obtained by the two methods. To quantitatively assess the difference between the two methods, a linear static model was first evaluated. This model was based on an earlier successful model of the accommodation and vergence system. The linear-model solution showed that these two methods were equivalent and thus could not account for the differences found. Then, a nonlinear static model, containing the deadspace operators depth of field and Panum's fusional area (PFA), was evaluated. Since two solutions were possible for each deadspace operator, there were four basic solutions. However, there were two binocular-viewing paradigms. This resulted in four prism-viewing and four lens-viewing solutions. Finally, a difference was taken between the prism- and lens-viewing measures, giving a total combination of 16 solutions. Only four of these solutions were equal to that using the phoria method. Some of the other solution lines were widely separated, thus providing a range of possible data values across different solution lines. Calculations showed that the variation in AC/A ratio values for data across difference solution lines was comparable to that found experimentally. Thus, the deadspace operators in the nonlinear model were able to account for the discrepancy between the AC/A ratio determined by the phoria and fixation disparity methods.

Comparison of linear and nonlinear statistical models for analyzing determinants of residential energy consumption

Data on individual daily feed intake, BW at 28-d intervals, and carcass composition were obtained on 1,212 crossbred steers. Within-animal regressions of cumulative feed intake and BW on linear and quadratic days on feed were used to quantify initial and ending BW, average daily observed feed intake (OFI), and ADG over a 120-d finishing period. Feed intake was predicted (PFI) with 3 biological simulation models (BSM): a) Decision Evaluator for the Cattle Industry, b) Cornell Value Discovery System, and c) NRC update 2000, using observed growth and carcass data as input. Residual feed intake (RFI) was estimated using OFI (RFI(EL)) in a linear statistical model (LSM), and feed conversion ratio (FCR) was estimated as OFI/ADG (FCR(E)). Output from the BSM was used to estimate RFI by using PFI in place of OFI with the same LSM, and FCR was estimated as PFI/ADG. These estimates were evaluated against RFI(EL) and FCR(E). In a second analysis, estimates of RFI were obtained for the 3 BSM as the difference between OFI and PFI, and these estimates were evaluated against RFI(EL). The residual variation was extremely small when PFI was used in the LSM to estimate RFI, and this was mainly due to the fact that the same input variables (initial BW, days on feed, and ADG) were used in the BSM and LSM. Hence, the use of PFI obtained with BSM as a replacement for OFI in a LSM to characterize individual animals for RFI was not feasible. This conclusion was also supported by weak correlations (<0.4) between RFI(EL) and RFI obtained with PFI in the LSM, and very weak correlations (<0.13) between RFI(EL) and FCR obtained with PFI. In the second analysis, correlations (>0.89) for RFI(EL) with the other RFI estimates suggest little difference between RFI(EL) and any of these RFI estimates. In addition, results suggest that the RFI estimates calculated with PFI would be better able to identify animals with low OFI and small ADG as inefficient compared with RFI(EL). These results may be due to the fact that computer models predict performance on an individual-animal basis in contrast to a LSM, which estimates a fixed relationship for all animals; hence, the BSM may provide RFI estimates that are closer to the true biological efficiency of animals. In addition, BSM may facilitate comparisons across different data sets and provide more accurate estimates of efficiency in small data sets where errors would be greater with a LSM.

This study builds upon two prior papers, which examine Arctic region bias of CAM3 (NCAR Community Atmosphere Model version 3) simulations during winter. CAM3 output is compared with ECMWF (European Centre for Medium-Range Weather Forecasts) 40 year reanalysis (ERA-40) data. Our prior papers considered the temperature and the vorticity equation terms and demonstrated that diabatic, transient, and linear terms dominate nonlinear bias terms over most areas of interest. Accordingly, this paper uses a linearized form of the model’s dynamical core equations to study aspects of the forcing that lead to the CAM3 biases. We treat the model’s long term winter bias as a solution to a linear stationary wave model (LSWM). Key features of the bias in the vorticity, temperature, and ln of surface pressure (=q) fields are shown at medium resolution. The important features found at medium resolution are captured at the much lower LSWM resolution. The Arctic q bias has two key features: excess q over the Barents Sea and a missing Beaufort High (negative maximum q bias) to the north of Alaska and eastern Siberia. The forcing fields are calculated by the LSWM. Horizontal advection tends to create multi-polar combinations of negative and positive extrema in the forcing. The positive and negative areas of forcing approximately match corresponding areas in the bias. There is a broad relation between cold bias with elevated q bias, as expected from classical theory. Forcing in related quantities: near surface vorticity and surface pressure combine to produce the sea level pressure bias.

Methods of estimating the vibrational effect of high-pressure pulses on the confuser of the complex technological pipeline have been presented. Hydrodynamic calculations are performed using the Ansys Fluent software package. To analyze the propagation of high-pressure pulses, time series of hydrodynamic variables have been constructed at several points of the model confuser located on the axis of the pipeline. Two linear stationary hydrodynamic models of the confuser have been constructed, and the possibility of their use in modeling the nonstationary propagation processes of high-pressure pulses has been studied. It has been established that, with an accuracy of more than 90%, the studied unsteady hydrodynamic processes in the confuser can be described by linear stationary models. An analysis of the amplitude–frequency characteristics of the confuser using these models showed that an approximately 100-bar impact on the confuser of pressure pulses is permissible and leads to pulsations of pressure with a signal-to-noise ratio of 110 dB, which does not exceed the maximum permissible level of pressure pulsations.

Falling in the elderly: Do statistical models matter for performance criteria of fall prediction? Results from two large population-based studies

To study the relationship between the linear statistical models we used methods of linear algebra, Hilbert spaces and statistics. It was found that there is a linear relationship between linear statistical models which is expressed by a matrix equality. Several corollaries are derived and discussed, and a new interpretation is proposed for the parameters of linear statistical model. The given relation between the linear statistical models may be useful for both theoretical analysis of statistical models and interpretation of applied statistical models, in particular, to analyze the impact of confounders.

It is well recognized that statistical linear interpolation models are computationally inexpensive and applicable to any climate data compared to the dynamic simulation method at regional scales. Using five different statistical linear interpolation models, we characterized each model’s performance to predict a climate variable of interest. General linear model, generalized additive model, spatial linear model, and bayesian spatial regression model (BSM) were analyzed. The climate variable of interest was the monthly precipitation, where the spatial variability was explained using terrain information: latitude, longitude, elevation, topographic aspect, and costal proximity. We used the root mean squared error, the mean absolute error and correlation coefficient as the performance. The BSM showed better performance in reflecting the spatial pattern of monthly precipitation compared to the other models. The monthly precipitation and its 95 % prediction interval on a 1 × 1 km grid spacing were generated through a spatial interpolation of 441 point observations.

Chapter 6 - Key Components of (Generalized) Linear Models: Statistical Distributions and the Linear Predictor

An important issue in statistical circuit design, other than the algorithms themselves, is the development of efficient, statistically valid element models. The authors first discuss what features are needed for a good statistical model. The standard FET model is shown to be difficult to use in a statistical simulation, due to the nonlinear relation between FET S-parameters and model parameters. A linear statistical FET model is then proposed that is based on principal component analysis. This linear model gives uncorrelated model parameters. In an example using measured S-parameter data from ninety 0.5- mu m GaAs FETs, 13 uncorrelated model parameters were needed to model the data from 1 to 11 GHz and at one bias. Simulation using this linear model and issues relating to bias are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Linear time series models have come to dominate the macroeconomic literature on rational expectations and equilibrium business cycle theory. But the explicit solution of such models has generally required strong restrictions upon the exogenous process of stochastic shocks (e.g., temporal independence) as well as upon the values of various demand and supply elasticities. This paper exhibits a solution technique, the method of z-transforms, which does not require one to impose such restrictions. The value of this method is illustrated by applying it to completely characterize the symmetric, stationary, rational expectations equilibria of a naive linear model of land speculation. This approach also permits systematic study of the informationally asymmetric equilibria of the model. THIS PAPER develops a method for analyzing rational expectations (RE) equilibria in linear economic models. The methods I shall discuss usually enable one to determine whether or not a given model has a RE equilibrium and, if one exists, to exhibit an explicit expression for the stochastic process of equilibrium prices. The techniques apply to linear models driven by stationary processes of exogenous random shocks.

The linear statistical model describes signals that are linear combinations of multiple modes. In this paper, we review the detection, estimation, and identification of such signals, paying special attention to the role played by projection operators and their low rank approximations. Projection operators provide a unified framework for several conventional concepts in signal processing and lead to new applications of the linear statistical model. Low rank approximations reduce computational requirements and broaden the range of practical uses for projections. As a point of departure, we discuss a VLSI chip we have developed for computing projections.

Two regression‐based methods that recalibrate the ECHAM4.5 general circulation model (GCM) output during austral summer have been developed for southern Africa, and their performance assessed over a 12‐year retroactive period 1989/90–2000/01. A linear statistical model linking near‐global sea‐surface temperatures (SSTs) to regional rainfall has also been developed. The recalibration technique is model output statistics (MOS) using principal components regression (PCR) and canonical correlation analysis (CCA) to statistically link archived records of the GCM to regional rainfall over much of Africa, south of the equator. The predictability of anomalously dry and wet conditions over each rainfall region during December–February (DJF) using the linear statistical model and MOS models has been quantitatively evaluated. The MOS technique outperforms the raw‐GCM ensembles and the linear statistical model. Neither the PCR‐MOS nor the CCA‐MOS models show clear superiority over the other, probably because the two methods are closely related. The need to recalibrate GCM predictions at regional scales to improve their skill at smaller spatial scales is further demonstrated in this paper. Copyright © 2006 Royal Meteorological Society.