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Estimating the prevalence of anemia rates among children under five in Peruvian districts with a small sample size

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Abstract

In this paper we attempt to answer the following question: “Is it possible to obtain reliable estimates for the prevalence of anemia rates in children under five years in the districts of Peru?” Specifically, the objective of the present paper is to understand to which extent employing the basic and the spatial Fay–Herriot models can compensate for inadequate sample size in most of the sampled districts, and whether the way of choosing the spatial neighbors has an impact on the resulting inference. Furthermore, we explore the question of how to choose an optimal way to define the neighbors. As such, our research focuses on studying the prediction accuracy of the aforementioned models, and on the sensitivity of the results to the definition of “neighbor”. We use the data from the Demographic and Family Health Survey of the year 2019, and the National Census carried out in 2017.

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Acknowledgments

The authors thank the reviewers for very thoughtful and helpful comments.

Funding

This research is supported by a grant from the Unidad de Investigación de la FIEECS-UNI.

Author information

Author notes

  1. Anna Sikov and José Cerda-Hernandez have contributed equally to this work.

Authors and Affiliations

  1. Department of Statistics, National Engineering University, Av. Tupac Amaru 210, Lima, Peru

    Anna Sikov

  2. Department of Economics, National Engineering University, Av. Tupac Amaru 210, Lima, Peru

    José Cerda-Hernandez

  3. Econometric modelling and data science research group-UNI, Lima, Peru

    Anna Sikov & José Cerda-Hernandez

Authors
  1. Anna Sikov
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  2. José Cerda-Hernandez
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Correspondence to Anna Sikov.

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Appendices

Appendix A

For this study, we use R software (see R Core Team 2020). The initial step was creating a SpatialPointsDataFrame object that encompasses both the geographic information and survey data. To accomplish this, we employed the SpatialPointsDataFrame function, which is available in the sp package (see Bivand et al. 2013), as follows.

proj=CRS("+proj=longlat +datum=WGS84 +no_defs")

data.sp=SpatialPointsDataFrame(coords=

cbind(data$Latitude,data$Longitude),

data=data,proj4string=proj)

To establish neighboring districts based on their geographical coordinates, it was employed the spdep package (see Pebesma and Bivand 2023). More precisely, it was utilized the knearneigh function which returns a list of the districts along with their corresponding K nearest neighbors.

neighbors<-knearneigh(coordinates(data.sp), k=K)

We use the list of the neighbors obtained in the output, in order to produce the matrix of spatial weights, W by assigning a weight of 1/K to each neighbor. Finally, the fh function from the emdi package (see Kreutzmann et al. 2019) was used to fit both the basic and spatial Fay Herriot models.

fh(fixed=formula, vardir="VR",

combined_data=data,domains="District",method = "reml",

correlation="spatial",corMatrix=W,

MSE=TRUE, mse_type = "spatialparbootbc")->spatial.fh

Here, the variables "VR" and "District" refer to the variance of the direct estimator and the identification district code, respectively. Note that omitting the third line would result in fitting the basic Fay Herriot model.

Appendix B

See Figs. 8 and 9.

Fig. 8
figure 8

The prevalence of anemia rates in children under five, per district, in varios departments in Peru

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Fig. 9
figure 9

The prevalence of anemia rates in children under five, per district, in varios departments in Peru

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Sikov, A., Cerda-Hernandez, J. Estimating the prevalence of anemia rates among children under five in Peruvian districts with a small sample size. Stat Methods Appl 32, 1779–1804 (2023). https://doi.org/10.1007/s10260-023-00698-x

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