More on detecting outliers
Detecting outliers in a uni-variate dataset
or series one may also apply a quick-and-dirty
diagnostic tool known as
Grubbs Test for Outliers
a.k.a. the maximum normed residual test
(after Snedercon and Cochran, 1989)
Grubbs Test
Department of Geography
UNIVERSITY OF FLORIDA, SPRING 2011
GEO 4167c section #6647 / GEO 6161 section # 8377
Intermediate Quantitative Methods
Instructor: Timothy J. Fik, Associate Professor
Prerequisite: GEO 3162 / GEO 6160 or equivalent
Time/Location: T
Geographical Analysis ISSN 0016-7363
Geographically Weighted Discriminant
Analysis
Chris Brunsdon,1 Stewart Fotheringham,2 Martin Charlton2
1
Department of Geography, University of Leicester, Leicester, U.K. 2National Centre for Geocomputation,
National U
Geographically Weighted Regression as a
Statistical Model
Chris Brunsdon
Stewart Fotheringham
Martin Charlton
October 6, 2000
Spatial Analysis Research Group
Department of Geography
University of Newcastle-upon-Tyne
Newcastle-Upon-Tyne UK
NE1 7RU
Abstract
Environment and Planning A 1998, volume 30, pages 1905-1927
Geographically weighted regression: a natural evolution
of the expansion method for spatial data analysis
A S F otheringham, M E Charlton
D epartment of Geography, University of Newcastle, Newcas
The Cartographic Journal
Vol. 43 No. 2
# The British Cartographic Society 2006
pp. 171179
July 2006
REFEREED PAPER
Mapping the Results of Geographically Weighted
Regression
Jeremy Mennis
Department of Geography and Urban Studies, Temple University, 1115 W
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserved.
Copyright 2000. All Rights Reserv
J Geogr Syst
DOI 10.1007/s10109-010-0123-7
ORIGINAL ARTICLE
The pyrogeography of sub-Saharan Africa: a study
of the spatial non-stationarity of reenvironment
relationships using GWR
Ana C. L. Sa Jose M. C. Pereira
Martin E. Charlton Bernardo Mota
Paulo
STAT 3523: MATRIX APPROACH TO REGRESSION ANALYSIS FALL 2007
Random Vectors and Matrices
A random vector or a random matrix contains elements that are random variables. Let Y denote an n 1 column vector:
Y =
Y1 . . . Yn
The expected value of Y is the v
Linear Probability Models and
Discrete Choice Models
Linear Probability Models (LPMs) and Discrete-Choice
Models (DCMs) typical fall under the rubric of
Categorical Response Models or
Binary Response Models
regression frameworks in which the dependent
va
International Journal of Epidemiology
International Epidemiological Association 1997
Vol. 26, No. 6
Printed in Great Britain
Regression Models for Ordinal
Responses: A Review of Methods
and Applications
CANDE V ANANTH* AND DAVID G KLEINBAUM
Ananth C V (T
Violation of Assumptions: Symptomatic of
a poor model or idiosyncrasies that lead to a general failure
of the model to explain variation in Y (the dependent variable)
use of an inappropriate estimation technique or procedure
using OLS when an alternati
Analysis of Spatial Pattern
Spatial Autocorrelation a primer
Involves the analysis of patterns or spatial data
to test for spatial dependence of a variable
with itself over space
auto self
autocorrelation how a variable is correlated
with itself spatiall
The Assessment of Leverage
The identification of significant outliers and
highly leveraged and/or influential sample
observations requires a further inspection
of various indices related to the Hat matrix.
A sample observation is said to be influential
wh
VI. Geographically Weighted Regression (GWR)
GWR is from the work of Fotheringham et al. (1998, 2000)
It is a regression-based modeling framework that generates
location-specific estimates for the estimated coefficients or
parameters (slope terms). In oth
Case #5a and 5b: Semi-log in X ( 1 > 0) shown in black
Semi-log in X ( 1 < 0) shown in red
Y
1 > 0
Function and transformation:
Y = 0 + 1 (log X)
Y = 0 - 1 (log X)
0
X
1 < 0
In general, semi-log models (in Y or X) are commonly
used to linearize a curvilin
II. Testing for Multicollinearity
When two or more independent variables in a regression
model are highly correlated with one another (or collinear),
they will contribute redundant explanatory information.
Hence, not all of those independent variables ne
Auto-Correlation Functions: A Primer
The Time-Series Trio
Lag
Autoregress
Ma
Correlograms
The simple lagged correlation coefficient rk of any
time-series variable can be generated and plotted
for specified time lags k (k=1,K) to develop what is
known as a
The Assessment of Leverage
The identification of significant outliers and
highly leveraged and/or influential sample
observations requires a further inspection
of various indices related to the Hat matrix.
A sample observation is said to be influential
wh
The Matrix Approach to Regression This document describes a matrix approach to regression. Throughout, we will let Y be an n 1 vector that is the response variable, X be the n (p + 1) matrix of the intercept and p explanatory variables, be the (p + 1) 1 v