Introduction

This assignment was for a Spatial Statistics class I took at Penn State. I carry out an analysis of mourning dove counts from section 7.4.2 of the Handbook of Spatial Statistics using tools from the \(geoRglm\) package. First, the assignments looks at the data through classical geostatistics and then moves onto more advanced topics.

Report Outline

  1. Project Description
  2. Research and Statistical Questions
  3. Variables of Interest
  4. Exploratory Data Analysis
  5. Statistical Analysis
  6. Recommendations

1. Project Description

From Handbook: As an illustrative example, consider data collected from the annual North American Breed-ing Bird Survey (BBS, see Robbins, Bystrak, and Geissler 1986). In this survey, conductedin May and June of each year, volunteer observers traverse roadside sampling routes thatare 39.2 km in length, each containing 50 stops. At each stop, the observer records the num-ber of birds (by species) seen and heard over a three-minute time span. There are several thousand BBS routes in North America. We focus on mourning dove (Zenaida macroura)counts from 45 routes in the state of Missouri as observed in 2007 and shown in Figure 7.4.Given the total count (aggregated over the 50 stops) of doves on the BBS route assigned to a spatial location at the route centroid, our goal is to produce a map of dove relative abundance within the state, as well as characterize the uncertainty associated with these predictions of relative abundance. Such maps are used to study bird/habitat relationships as well as species range.

2. Research and Statistical Questions

Research Questions
  1. How to characterize the uncertainty associated with predictions of relative abundance
  2. Understadning maps to study bird/habitat relatioships and species range.
Statistical Questions
  1. Appropriate Model for Data
  2. Model Diagnostics for Model

3. Variables of Interest

Slide 8 from Lecture 8 gives us the three layers of the hierarchical model:

\[f(\eta, \theta | Y) \propto f(Y | \eta, \theta) \times f(\eta | \theta) \times \pi(\theta)\]

In english, our unobserved process of interest, where Y denotes our data, \(\eta\) the process, \(\theta\) the parameters is prorportional to our Data Model times the Process Model times Parameter Model.

\[f(Y | \eta, \theta) : Y(S_i) | \lambda(S_i) \sim Pois(\lambda(S_i)\] \[f(\eta | \theta) : \lambda(S_i) \sim GP(\beta, \eta(S_i))\] \[\pi(\phi) : \phi \sim U(500, 300,000)\]

Question 2

Estimates for the OLS model are found here:

Estimating the variogram nonparametrically and then fitting an exponential variogram

[width=210pt]{nonpar1.jpg} [width=210pt]{fitvg2.jpg}

The parameter estimates are \(\hat{\sigma^2}\)=5.18, \(\hat{\rho}\)=61.08 and \(\hat{\tau^2}\)=1.22.

Appendix