Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Non-testability of equal weights spatial dependence

We show that any invariant test for spatial autocorrelation in a spatial error or spatial lag model with equal weights matrix has power equal to size. This result holds under the assumption of an elliptical distribution. Under Gaussianity, we also show that any test whose power is larger than its size for at least one point in the parameter space must be biased.

The observed relationships between wheat and climate in China

Recent changes in climate have had a measurable impact on crop yield in China. The objective of this study is to investigate how climate variability affects wheat yield in China at different spatial scales. First the response of wheat yield to the climate at the provincial level from 1978 to 1995 for China was analysed. Wheat yield variability was only correlated with climate variability in some regions of China. At the provincial level, the variability of precipitation had a negative impact on wheat yield in parts of southeast China, but the seasonal mean temperature had a negative impact on wheat yield in only a few provinces, where significant variability in precipitation explained about 23–60% of yield variability, and temperature variability accounted for 37–41% of yield variability from 1978 to 1995. The correlation between wheat yield and climate for the whole of China from 1985 to 2000 was investigated at five spatial scales using climate data. The Climate Research Unit (CRU) and National Centers for Environmental Prediction (NCEP) proportions of the grid cells with a significant yield–precipitation correlation declined progressively from 14.6% at 0.5° to 0% at 5° scale. In contrast, the proportion of grid cells significant for the yield–temperature correlation increased progressively from 1.9% at 0.5° scale to 16% at 5° scale. This indicates that the variability of precipitation has a higher association with wheat yield at small scales (0.5°, 2°/2.5°) than at larger scales (4°/5.0°); but wheat yield has a good association with temperature at all levels of aggregation. The precipitation variable at the smaller scales (0.5°, 2°/2.5°) is a dominant factor in determining inter-annual wheat yield variability more so than at the larger scales (4°/5°). We conclude that in the current climate the relationship between wheat yield and each of precipitation and temperature becomes weaker and stronger, respectively, with an increase in spatial scale.

Testing for spatial autocorrelation: the regressors that make the power disappear

We show that for any sample size, any size of the test, and any weights matrix outside a small class of exceptions, there exists a positive measure set of regression spaces such that the power of the Cli-Ord test vanishes as the autocorrelation increases in a spatial error model. This result extends to the tests that dene the Gaussian power envelope of all invariant tests for residual spatial autocorrelation. In most cases, the regression spaces such that the problem occurs depend on the size of the test, but there also exist regression spaces such that the power vanishes regardless of the size. A characterization of such particularly hostile regression spaces is provided.

The spatial distribution of carbon dioxide in an environmental test chamber

The spatial distribution of CO2 level in a classroom carried out in previous field work research has demonstrated that there is some evidence of variations in CO2 concentration in a classroom space. Significant fluctuations in CO2 concentration were found at different sampling points depending on the ventilation strategies and environmental conditions prevailing in individual classrooms. However, how these variations are affected by the emitting sources and the room air movement remains unknown. Hence, it was concluded that detailed investigation of the CO2 distribution need to be performed on a smaller scale. As a result, it was decided to use an environmental chamber with various methods and rates of ventilation, for the same internal temperature and heat loads, to study the effect of ventilation strategy and air movement on the distribution of CO2 concentration in a room. The role of human exhalation and its interaction with the plume induced by the body's convective flow and room air movement due to different ventilation strategies were studied in a chamber at the University of Reading. These phenomena are considered to be important in understanding and predicting the flow patterns in a space and how these impact on the distribution of contaminants. This paper attempts to study the CO2 dispersion and distribution at the exhalation zone of two people sitting in a chamber as well as throughout the occupied zone of the chamber. The horizontal and vertical distributions of CO2 were sampled at locations with a probability that CO2 variation is considered high. Although the room size, source location, ventilation rate and location of air supply and extract devices all can have influence on the CO2 distribution, this article gives general guidelines on the optimum positioning of CO2 sensor in a room.

Electrophysiological correlates of spatial orienting towards angry faces: a source localization study

The goal of this study was to examine behavioral and electrophysiological correlates of involuntary orienting toward rapidly presented angry faces in non-anxious, healthy adults using a dot-probe task in conjunction with high-density event-related potentials and a distributed source localization technique. Consistent with previous studies, participants showed hypervigilance toward angry faces, as indexed by facilitated response time for validly cued probes following angry faces and an enhanced P1 component. An opposite pattern was found for happy faces suggesting that attention was directed toward the relatively more threatening stimuli within the visual field (neutral faces). Source localization of the P1 effect for angry faces indicated increased activity within the anterior cingulate cortex, possibly reflecting conflict experienced during invalidly cued trials. No modulation of the early C1 component was found for affect or spatial attention. Furthermore, the face-sensitive N170 was not modulated by emotional expression. Results suggest that the earliest modulation of spatial attention by face stimuli is manifested in the P1 component, and provide insights about mechanisms underlying attentional orienting toward cues of threat and social disapproval.