Residual Autocorrelation Research Articles

Long-term exposure to air pollution and COVID-19 incidence: A multi-country study

The study of the impacts of air pollution on COVID-19 has gained increasing attention. However, most of the existing studies are based on a single country, with a high degree of variation in the results reported in different papers. We attempt to inform the debate about the long-term effects of air pollution on COVID-19 by conducting a multi-country analysis using a spatial ecological design, including Canada, Italy, England and the United States. The model allows the residual spatial autocorrelation after accounting for covariates. It is concluded that the effects of PM2.5 and NO2 are inconsistent across countries. Specifically, NO2 was not found to be an important factor affecting COVID-19 infection, while a large effect for PM2.5 in the US is not found in the other three countries. The Population Attributable Fraction for COVID-19 incidence ranges from 3.4% in Canada to 45.9% in Italy, although with considerable uncertainty in these estimates.

Forecasting the conditional heteroscedasticity of stock returns usingasymmetric models based on empirical evidence from Eastern Europeancountries: Will there be an impact on other industries?

This empirical study investigates the leverage effect in six Eastern European countries under normal and non-normaldistribution densities for the sample period from January 2020 to August 2020. We find three countries, Bulgaria, CzechRepublic and Russia which are subject to ARCH effect whereas Poland, Romania and Hungary do not exhibit ARCHeffect in daily stock returns. Further, our study finds leverage effect, where past bad news affects is asymmetrical, pastnegative returns cause more volatility in current stock returns as compared to past positive returns, in three EasternEuropean countries. Based on the AIC and BIC model selection criteria we find that the non-normal student t-distributionand GED produce reliable estimates for Bulgaria, Czech Republic and Poland, respectively. The autocorrelation functionQ1 statistic confirms the insignificance of autocorrelation in residuals of TGARCH model. The impact of stock marketdynamics on other industries, such as pharmaceutical industry, textile and clothing industry, automotive industry issignificant, especially in the conditions of COVID-19 pandemic

English

The main objective of this paper is to examine the effects of interest rate on economic growth in Gambia over the period 1993 to 2017. The Vector E rror Correction Model (VECM) is used to check the relationships between the dependent variable (Gross Domestic Product) and independent variables (Real Effective Exchange Rate and Real Interest Rate), both in the short-run and long-run. Post estimation tests, including Lagrange Multiplier test for residual autocorrelation were also conducted for autocorrelation, as well as Jarque Bera to test for stability and to check whether residuals are normally distributed. The empirical evidence indicates that there is no short-run association between the growth of the Gambian economy and interest rate but that there is a long run connection that runs from real interest rate and real exchange rate to GDP. Based on these findings, the paper recommends for the government through the Ministry of Finance and Economic Affairs to prudently manage the Gambia’s budget by avoiding unnecessary expenditures that could lead to budget deficits.These budget deficits are key drivers that cause interest rates to rise, which in turn are inimical to economic growth.   Key words: Gross domestic product, real interest rate, real exchange rate, Vector Error Correction Model (VECM).

The effect of sociodemographic factors on COVID-19 incidence of 342 cities in China: a geographically weighted regression model analysis

BackgroundSince December 2019, the coronavirus disease 2019 (COVID-19) has spread quickly among the population and brought a severe global impact. However, considerable geographical disparities in the distribution of COVID-19 incidence existed among different cities. In this study, we aimed to explore the effect of sociodemographic factors on COVID-19 incidence of 342 cities in China from a geographic perspective.MethodsOfficial surveillance data about the COVID-19 and sociodemographic information in China’s 342 cities were collected. Local geographically weighted Poisson regression (GWPR) model and traditional generalized linear models (GLM) Poisson regression model were compared for optimal analysis.ResultsCompared to that of the GLM Poisson regression model, a significantly lower corrected Akaike Information Criteria (AICc) was reported in the GWPR model (61953.0 in GLM vs. 43218.9 in GWPR). Spatial auto-correlation of residuals was not found in the GWPR model (global Moran’s I = − 0.005, p = 0.468), inferring the capture of the spatial auto-correlation by the GWPR model. Cities with a higher gross domestic product (GDP), limited health resources, and shorter distance to Wuhan, were at a higher risk for COVID-19. Furthermore, with the exception of some southeastern cities, as population density increased, the incidence of COVID-19 decreased.ConclusionsThere are potential effects of the sociodemographic factors on the COVID-19 incidence. Moreover, our findings and methodology could guide other countries by helping them understand the local transmission of COVID-19 and developing a tailored country-specific intervention strategy.

Evaluating the NDVI–Rainfall Relationship in Bisha Watershed, Saudi Arabia Using Non-Stationary Modeling Technique

The Normalized Difference Vegetation Index (NDVI) and rainfall data were used to model the spatial relationship between vegetation and rainfall. Their correlation in previous studies was typically based on a global regression model, which assumed that the correlation was constant across space. The NDVI–rainfall association, on the other hand, is spatially non-stationary, non-linear, scale-dependent, and influenced by local factors (e.g., soil background). In this study, two statistical methods are used in the modeling, i.e., traditional ordinary least squares (OLS) regression and geographically weighted regression (GWR), to evaluate the NDVI–rainfall relationship. The GWR was implemented annually in the growing seasons of 2000 and 2016, using climate data (Normalized Vegetation Difference Index and rainfall). The NDVI–rainfall relationship in the studied Bisha watershed (an eco-sensitive zone with a complex landscape) was found to have a stable operating scale of around 12 km. The findings support the hypothesis that the OLS model’s average impression could not accurately represent local conditions. By addressing spatial non-stationarity, the GWR approach greatly improves the model’s accuracy and predictive ability. In analyzing the relationship between NDVI patterns and rainfall, our research has shown that GWR outperforms a global OLS model. This superiority stems primarily from the consideration of the relationship’s spatial variance across the study area. Global regression techniques such as OLS can overlook local details, implying that a large portion of the variance in NDVI is unexplained. It appears that rainfall is the most significant factor in deciding the distribution of vegetation in these regions. Furthermore, rainfall had weak relationships with areas predominantly located around wetlands, suggesting the need for additional factors to describe NDVI variations. The GWR method performed better in terms of accuracy, predictive power, and reduced residual autocorrelation. Thus, GWR is recommended as an explanatory and exploratory technique when relations between variables are subject to spatial variability. Since the GWR is a local form of spatial analysis that aligned to local conditions, it has the potential for more accurate prediction; however, a larger amount of data is needed to allow a reliable local fitting.

Accommodating the role of site memory in dynamic species distribution models.

First-order dynamic occupancy models (FODOMs) are a class of state-space model in which the true state (occurrence) is observed imperfectly. An important assumption of FODOMs is that site dynamics only depend on the current state and that variations in dynamic processes are adequately captured with covariates or random effects. However, it is often difficult to understand and/or measure the covariates that generate ecological data, which are typically spatiotemporally correlated. Consequently, the non-independent error structure of correlated data causes underestimation of parameter uncertainty and poor ecological inference. Here, we extend the FODOM framework with a second-order Markov process to accommodate site memory when covariates are not available. Our modeling framework can be used to make reliable inference about site occupancy, colonization, extinction, turnover, and detection probabilities. We present a series of simulations to illustrate the data requirements and model performance. We then applied our modeling framework to 13yr of data from an amphibian community in southern Arizona, USA. In this analysis, we found residual temporal autocorrelation of population processes for most species, even after accounting for long-term drought dynamics. Our approach represents a valuable advance in obtaining inference on population dynamics, especially as they relate to metapopulations.

Spatial distribution of carbon storage in natural secondary forest based on geographically weighted regression expansion model.

To accurately assess carbon storage and its spatial distribution in natural secondary forest at the regional scale, we constructed seven expansion models by modifying the geographically weighted regression (GWR) in aspects of spatial dimension, parameter heterogeneity and residual spatial autocorrelation, based on data collected from 165 bureau level permanent plots in Langxi Forest Farm of Wangqing Forestry Bureau in Jilin Province. Stand factor, topography factor, and soil factor were selected as the influencing factors. The expansion models included geographically and altitudinal weighted regression (GAWR), semiparametric geographically weighted regression (SGWR), semiparametric geographically and altitudinal weighted regression (SGAWR), geographically weighted regression Kriging (GWRK), geographically and altitudinal weighted regression Kriging (GAWRK), semiparametric geographically weighted regression Kriging (SGWRK), and semiparametric geographically and altitudinal weighted regression Kriging (SGAWRK). Coefficient of determination (R2), mean square error (MSE) and Akaike's Information Criterion (AIC) were used to evaluate the fitness of these models. Finally, the spatial distribution diagram of forest carbon storage was drawn with the fitting results of the optimal regression model, and the distribution pattern of forest carbon storage in the research area was analyzed. The stand factor and topographic factor had strong influence on carbon storage of natural secondary forests, among which the average diameter at breast height (DBH) of stands was the dominant variable. There was positive correlation between stand factor and topographic factor. SGWR and SGAWR model could reduce the spatial autocorrelation of the GWR model residual. The geographically regression expansion model could improve the fitting effect of GWR model. Among them, the SGWRK model had the highest R2 and the lowest MSE and AIC. The method with altitude as the spatial weight did not effectively improve the fitting effect of the model. The total forest carbon storage of Langxi Forest Farm was 205×104 t, and the carbon density ranged from 8.56 to 145.74 t·hm-2, with a mean value of 57.98 t·hm-2. Overall, the distribution pattern of carbon storage was high in the northwest and low in the southeast, while high in the edge and low in the interior. By improving the parameter heterogeneity and residual spatial autocorrelation in the GWR model, we can accurately assess the spatial relationship between forest carbon storage and relevant variables in the study area, and improve the estimation accuracy of the forest carbon storage and its spatial distribution at the regional scale.

Predicting the magnitude of residual spatial autocorrelation in geographical ecology

The level of spatial autocorrelation (SAC) present in model residuals can have a detrimental influence on statistical inferences in geographical ecology. There has been significant progress in understanding the nature and causes of residual SAC and developing new methods to reduce the SAC. However, ecologists have not yet found a suitable answer as to when the level of residual autocorrelation is likely to magnify and whether its shift through spatial regression (i.e. the difference in the residual SAC produced by non‐spatial and spatial approaches) can be predicted using a set of readily available variables. In this paper, I reanalyzed the outcomes reported by Bini et al. (2009), who originally compared the differences in the standardized regression coefficients resulting from non‐spatial ordinary least squares and various spatially explicit methods. Although these researchers were unable to identify reliable predictors of the coefficient shifts, in the present study, I observed that the level of residual autocorrelation significantly and linearly increased with an increase in the magnitude of the SAC inherently possessed by, especially, response and explanatory variables. Moreover, the amount of shift in the residual SAC varied as a linear function of the response and explanatory variables. These findings imply that, in general, specific conditions exist under which there is an increase in the magnitude of the residual SAC, that such a shift can be predicted by the nature and structure of the data sets involved, and that, after all, the residual SAC varies systematically regardless of the selection of the data type, statistical method and spatial scale. I suggest that the level of the SAC present in the input variables can directly indicate how much improvement (i.e. reduction in the residual SAC) a non‐spatial model will experience when a proper spatial approach is employed.

Irrelevance of inflation: the 20 Fama-French stocks

Purpose - The relation between inflation and stock returns has been widely scrutinized. Its importance transcends finding just a simple relation, and has repercussions on the conduct of monetary policy. Theoretically, the relation should be positive and one-to-one. However, early on, the empirical relation was found to be statistically significantly negative. This paper contributes to the theoretical and empirical debate. The null hypothesis is that inflation is irrelevant to stock returns. Therefore, neither a positive theoretical, nor a negative empirical relation, should robustly hold. This position is in accordance to the basic principles of modern corporate finance, which state that the real and nominal equity values are equal. Methodology - The paper starts with simple correlations and presents the probability distributions and histograms of all variables. All distributions are characterized by significant outliers. A theoretical model that excludes inflation is introduced, and the statistical significance of including inflation is tested. The quest covers the 20 Fama-French stock portfolios, classified by their percentiles of equity values. Hence, both bilateral and multilateral regressions are carried out. Findings – Initially bilateral correlations were found to be negative consistent with the early empirical evidence. However, by using robust standard errors, robust least squares, and quantile regressions, the evidence is totally reversed. There is strong support for the irrelevance of inflation. This is true if the investor is sophisticated, i.e. she does not give too much attention to simple bilateral correlations, if she utilizes advanced economic procedures like robust least squares and quantile regressions, if she adjusts for residual autocorrelation and heteroscedasticity, and if she incorporates fundamental variables in the estimation process. Conclusion - Hence the prima facie evidence of non-neutrality is challenged by this paper’s analysis. In opposition to the conviction of many economists, and despite their inherent resistance, the paper argues for inflation irrelevance.

Estimating monthly air temperature using remote sensing on a region with highly variable topography and scarce monitoring in the southern Ecuadorian Andes

Monitoring of air temperature has implications in a wide range of environmental applications. Air temperature commonly measured with meteorological stations provides a high accuracy and temporal resolution for specific monitoring sites. However, in regions with highly variable topography and scare monitoring such as the case of the southern Ecuadorian Andes, these in situ data poorly describe the spatial variability of air temperature. Thus, remote sensing data has a great potential to estimate the spatial distribution of climatological variables due to the spatial continuity of the information. This research aims to estimate the spatial distribution of the monthly air temperature in the Paute river basin for the period 2014–2017, using statistical and geostatistical methods: linear regression (LR), random forest regression (RF), and regression kriging (RK), in addition to evaluate the use of altitude and other auxiliary variables (land surface temperature, latitude, and longitude). Cross-validation showed that RF performed better than LR as well as when using auxiliary variables compared to only the altitude (LR-altitude: RMSE=1.325 °C, P bias= −0.150%, r=0.775; LR-auxiliary variables: RMSE=1.265 °C, P bias=0.000% r=0.795; RF-altitude: RMSE=1.235 °C, P bias =0.200%, r=0.810; RF-auxiliary variables RMSE=1.205 °C, P bias =0.200%, r=0.820). The application of regression kriging was limited since less than 50% of the months had spatial autocorrelation in the regression model residuals. Nevertheless, in these months, regression kriging increased the estimation performance. The outcomes of this research work increase the understanding of the spatial distribution of monthly air temperature in the Paute river basin, which will improve hydrological modeling.

The Impact of Weather Factors on Quotations of Energy Sector Companies on Warsaw Stock Exchange

Recent researches on behavioral finance have tested for, among others, evidence for the relations between weather, investors’ mood, and investment decisions. Many of the researches related to the influence of some weather factors, such as sunshine duration on stock exchange returns, but there is no complex research taking into account a wide group of weather factors determining investors’ mood. The main goal of the article is to verify the influence of weather factors on basic market parameters of energy sector companies quoted on the Warsaw Stock Exchange. Rates of return, trading volumes, and values of trading volume are taken into account during the research. All analyses are based on econometric models assuming the existence of typical problems of estimation such as: autocorrelation of residuals, heteroskedasticity, or abnormality of residuals. The best approximation of models was obtained for GARCH (Generalized Autoregressive Conditional Heteroskedasticity) type models.

Time series analysis of the enhanced vegetation index to detect coffee crop development under different irrigation systems

The coffee crop spectral behavior identification throughout its cycle can contribute to its development monitoring under pest incidence. We aim to identify coffee development through time signatures of enhanced vegetation index (EVI), as well as to evaluate the use of seasonal autoregressive integrated moving average (SARIMA) models to identify coffee trees spectrum-time patterns under different irrigation management and design future scenarios. Three coffee fields were selected under different irrigation systems, whose EVI data of 8 years were obtained from the moderate resolution image spectroradiometer sensor. Each coffee crop model was subjected to residual autocorrelation test and classified according to information criteria, while its accuracy was assessed by means of prediction error measures and agreement index. The estimated and observed EVI values were similar, even for the predicted year. However, in agricultural years during which coffee diseases occurred, the crops showed vegetative vigor below the expected. We concluded that SARIMA models enabled the establishment of a reliable spectral signature expected for coffee crop, which could help with crop management defining, regardless of the irrigation system adopted. Based on the evaluation of divergence between expected and observed spectral signatures, early signs of coffee underdevelopment were detected, which could reduce economic loss risks on its commercial chain.

Low spatial autocorrelation in mountain biodiversity data and model residuals

AbstractSpatial autocorrelation (SAC) is a common feature of ecological data where observations tend to be more similar at some geographic distance(s) than expected by chance. Despite the implications of SAC for data dependencies, its impact on the performance of species distribution models (SDMs) remains controversial, with reports of both strong and negligible impacts on inference. Yet, no study has comprehensively assessed the prevalence and the strength of SAC in the residuals of SDMs over entire geographic areas. Here, we used a large‐scale spatial inventory in the western Swiss Alps to provide a thorough assessment of the importance of SAC for (1) 850 species belonging to nine taxonomic groups, (2) six predictors commonly used for modeling species distributions, and (3) residuals obtained from SDMs fitted with two algorithms with the six predictors included as covariates. We used various statistical tools to evaluate (1) the global level of SAC, (2) the spatial pattern and spatial extent of SAC, and (3) whether local clusters of SAC can be detected. We further investigated the effect of the sampling design on SAC levels. Overall, while environmental predictors expectedly displayed high SAC levels, SAC in biodiversity data was rather low overall and vanished rapidly at a distance of ~5–10 km. We found low evidence for the existence of local clusters of SAC. Most importantly, model residuals were not spatially autocorrelated, suggesting that inferences derived from SDMs are unlikely to be affected by SAC. Further, our results suggest that the influence of SAC can be reduced by a careful sampling design. Overall, our results suggest that SAC is not a major concern for rugged mountain landscapes.

Are human natal sex ratio differences across the world adaptive? A test of Fisher's principle

Fisher's principle states that natural selection favours an equal number of male and female births at the population level, unless there are sex differences in rearing costs or sex differences in mortality before the end of the period of parental investment. Sex differences in rearing costs should be more pronounced in low- than in high-resource settings. We, therefore, examined whether human development index and sex differences in child mortality contribute to the natural variation in human sex ratio at birth across the globe. As predicted by Fisher's principle, the proportion of male births increased with both increasing male-biased childhood mortality and level of development of each country. However, these relationships were absent after accounting for spatial autocorrelation in the residuals, which our inference is conditioned on. This work shows how the failure to account for residual spatial autocorrelation can lead to incorrect conclusions regarding support for predictions from sex allocation theory.

Beyond linearity, stability, and equilibrium: The edm package for empirical dynamic modeling and convergent cross-mapping in Stata

How can social and health researchers study complex dynamic systems that function in nonlinear and even chaotic ways? Common methods, such as experiments and equation-based models, may be ill-suited to this task. To address the limitations of existing methods and offer nonparametric tools for characterizing and testing causality in nonlinear dynamic systems, we introduce the edm command in Stata. This command implements three key empirical dynamic modeling (EDM) methods for time series and panel data: 1) simplex projection, which characterizes the dimensionality of a system and the degree to which it appears to function deterministically; 2) S-maps, which quantify the degree of nonlinearity in a system; and 3) convergent cross-mapping, which offers a nonparametric approach to modeling causal effects. We illustrate these methods using simulated data on daily Chicago temperature and crime, showing an effect of temperature on crime but not the reverse. We conclude by discussing how EDM allows checking the assumptions of traditional model-based methods, such as residual autocorrelation tests, and we advocate for EDM because it does not assume linearity, stability, or equilibrium.

Food safety knowledge, attitudes and practices of food handlers: A cross-sectional study in school kitchens in Esp\xedrito Santo, Brazil

BackgroundThe adoption and evaluation of good practices in food handling in food service are essential to minimizing foodborne diseases. The present study aimed to evaluate food safety knowledge, attitudes, and practices of food handlers in schools in Vitória, Brazil.MethodsA cross-sectional study was carried out in the school food services of the municipal network of Vitória-ES. The sample of food handlers was obtained by convenience and comprised food handlers involved with preparation and other kitchen-related activities. The instrument consisted of a structured questionnaire with 36 six questions that included sociodemographic characteristics, knowledge, attitudes, and practices (KAP) related to good practices and food safety. The questionnaire was answered by 172 food handlers. Pearson correlation test, T-test, Tukey’s test and multiple linear regression analysis were conducted. Data entry and analysis were done using SPSS v.20 software.ResultsMost of the participants were female (96.5%, n = 166), were 40 to 49 years old (44.8%, n = 78), attended high school (57.9%, n = 99), had up to 5 years of experience in the role (39.5%, n = 68). Some of them had participated at least 4 times in training (74.4%, n = 128) of which the most recent session had occurred within 3 months (52.0%, n = 44). The lowest score was obtained for knowledge (7.1 ± 1.22). All the models presented significant results for the F-test. This result show good model fit and results ranging from 1.5 to 2.5 on the Durbin Watson test of residual autocorrelation. The linear regression analysis allowed us to identify that the knowledge score increased with experience, but it was significant only for those who had spent up to 10 years in the role. The knowledge score was associated with experience and training time. Attitudes were significantly related to the schooling and training time. The increase in the classification of practices is shown only through a classification of attitudes.ConclusionsAlthough the food handlers’ knowledge level in general was considered as sufficient, it was inferior to their scores for attitudes and practices regarding certain food safety concepts. Food safety training is ongoing in these units and covers the main aspects that favour the transformation of knowledge into appropriate attitudes and practices.

Creating virtual species to test species distribution models: the importance of landscape structure, dispersal and population processes

The use of virtual species to test species distribution models is important for understanding how aspects of the model development process influence model performance. Typically, virtual species are simulated by defining their niche as a function of environmental variables and simulating occurrence probabilistically via Bernoulli trials. This approach ignores endogenous processes known to drive species distribution such as dispersal and population dynamics. To understand whether these processes are important for simulating virtual species we compared the probabilistic simulation approach to those incorporating endogenous processes. This comparison was done by evaluating changes in the relationship between species occurrence and habitat suitability over a number of landscapes with varying spatial structure. We found that the combined effects of population dynamics and dispersal meant the probability of occurrence of a single cell was not only dependent on habitat suitability, but also the number of occupied cells nearby. This resulted in a dependence on the size of clusters of high suitability cells (analogous to patch size) to maintain populations, increased residual spatial autocorrelation and non‐stationarity of the species response between landscapes. These data characteristics are attributes of real species distribution data and are not present in probabilistic simulations. Researchers using virtual species should consider the importance of these characteristics to their study objectives to decide whether the inclusion of endogenous processes is necessary.

An adaptive model for security prices driven by latent values: parameter estimation and option pricing effects

We develop a model where the log of stock price is regressive to latent intrinsic value. The model is similar to an Ornstein–Uhlenbeck model but differs in that log price reverts to stochastic intrinsic value. Since intrinsic value is latent, we use a Kalman filter to estimate parameters. The model generates autocorrelated residuals and the Kalman filter yields volatility estimates that are considerably different from those that assume log price differences are independent. We price calls using both the standard estimators and those derived from the Kalman filter to demonstrate the impact of inappropriate estimation techniques. We estimate parameters for selected stocks and test delta hedging performance versus alternative models.

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

Comment on Pescott & Jitlal 2020: Failure to account for measurement error undermines their conclusion of a weak impact of nitrogen deposition on plant species richness.

Estimation of the impacts of atmospheric nitrogen (N) deposition on ecosystems and biodiversity is a research imperative. Analyses of large-scale spatial gradients, where an observed response is correlated with measured or modelled deposition, have been an important source of evidence. A number of problems beset this approach. For example, if responses are spatially aggregated then treating each location as statistically independent can lead to biased confidence intervals and a greater probably of false positive results. Using methods that account for residual spatial autocorrelation, Pescott & Jitlal (2020) re-analysed two large-scale spatial gradient datasets from Britain where modelled N deposition at 5 × 5 km resolution had been previously correlated with species richness in small quadrats. They found that N deposition effects were weaker than previously demonstrated leading them to conclude that “previous estimates of Ndep impacts on richness from space-for-time substitution studies are likely to have been over-estimated”. We use a simulation study to show that their conclusion is unreliable despite them recognising that an influential fraction of the residual spatially structured variation could itself be attributable to N deposition. This arises because the covariate used was modelled N deposition at 5 × 5 km resolution leaving open the possibility that measured or modelled N deposition at finer resolutions could explain more variance in the response. Explicitly treating this as spatially auto-correlated error ignores this possibility and leads directly to their unreliable conclusion. We further demonstrate the plausibility of this scenario by showing that significant variation in N deposition at the 1 km square resolution is indeed averaged at 5 × 5 km resolution. Further analyses are required to explore whether estimation of the size of the N deposition effect on plant species richness and other measures of biodiversity is indeed dependent on the accuracy and hence measurement error of the N deposition covariate. Until then the conclusions of Pescott & Jitlal (2020) should be considered premature.