Estimating range of influence in case of missing spatial data: a simulation study on binary data

BackgroundThe range of influence refers to the average distance between locations at which the observed outcome is no longer correlated. In many studies, missing data occur and a popular tool for handling missing data is multiple imputation. The objective of this study was to investigate how the estimated range of influence is affected when 1) the outcome is only observed at some of a given set of locations, and 2) multiple imputation is used to impute the outcome at the non-observed locations.MethodsThe study was based on the simulation of missing outcomes in a complete data set. The range of influence was estimated from a logistic regression model with a spatially structured random effect, modelled by a Gaussian field. Results were evaluated by comparing estimates obtained from complete, missing, and imputed data.ResultsIn most simulation scenarios, the range estimates were consistent with ≤25% missing data. In some scenarios, however, the range estimate was affected by even a moderate number of missing observations. Multiple imputation provided a potential improvement in the range estimate with ≥50% missing data, but also increased the uncertainty of the estimate.ConclusionsThe effect of missing observations on the estimated range of influence depended to some extent on the missing data mechanism. In general, the overall effect of missing observations was small compared to the uncertainty of the range estimate.

[1]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[2]  Patrick Royston,et al.  Multiple imputation using chained equations: Issues and guidance for practice , 2011, Statistics in medicine.

[3]  A. Ersbøll,et al.  The range of influence between cattle herds is of importance for the local spread of Salmonella Dublin in Denmark. , 2008, Preventive veterinary medicine.

[4]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[5]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[6]  L. Tierney,et al.  Accurate Approximations for Posterior Moments and Marginal Densities , 1986 .

[7]  Lena Osterhagen,et al.  Multiple Imputation For Nonresponse In Surveys , 2016 .

[8]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[9]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[10]  Russell V. Lenth,et al.  Statistical Analysis With Missing Data (2nd ed.) (Book) , 2004 .

[11]  日野 寛三,et al.  対数正規分布(Lognormal Distribution)のあてはめについて , 1994 .

[12]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[13]  Paul T. von Hippel.  Regression with missing Ys: An improved strategy for analyzing multiply imputed data , 2007 .