Modelling spatial processes: the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Lecture notes in earth sciences
87 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 167 S. graph. Darst., Kt. |
| ISBN: | 3540662081 |
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| 100 | 1 | |a Tiefelsdorf, Michael |d 1958- |e Verfasser |0 (DE-588)12131328X |4 aut | |
| 245 | 1 | 0 | |a Modelling spatial processes |b the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables |c Michael Tiefelsdorf |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a XVIII, 167 S. |b graph. Darst., Kt. | ||
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1
THE ORIGINS OF THE EXACT APPROACH . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 2 1.2 ORGANIZATION OF THE MONOGRAPH . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 6 I UNDERLYING CONCEPTS OF
SPATIAL PROCESSES 2 THE REGRESSION MODEL . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 13 2.1 A REVIEW OF
ORDINARY LEAST S QUARES . . . . . . . . . . . . . . . . . . . . . . . .
. . . 13 2.2 ORDINARY LEAST S QUARES WITH CORRELATED DISTURBANCES . . .
. . . . . . . 17 2.3 THE IMPACT OF UNACCOUNTED VARIABLES . . . . . . . .
. . . . . . . . . . . . . . . . . 18 2.3.1 THE TWO S TAGE ESTIMATION
PROCEDURE . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.2 THE
MISSPECIFIED REGRESSION MODEL . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 20 3 THE SPECIFICATION OF SPATIAL RELATIONS . . . . . . .
. . . . . . . . . . . . 23 3.1 IMPLEMENTATION OF S PATIAL S TRUCTURES .
. . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 TYPOLOGY OF S
PATIAL OBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 24 3.1.2 RELATIONS BETWEEN S PATIAL OBJECTS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 25 3.1.3 S IMILARITY VERSUS
DISSIMILARITY RELATIONS . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.4 FUNCTIONAL RELATIONSHIPS IN RELATIVE S PACE . . . . . . . . . . .
. . . . . . . . . . 28 3.1.5 CODING S CHEMES OF S PATIAL S TRUCTURE
MATRICES . . . . . . . . . . . . . . . . . 29 3.2 S OME S PECIAL S
PATIAL S TRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 31 3.2.1 REGULAR S PATIAL S TRUCTURES . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 31 3.2.2 HIGHER ORDER LINK
MATRICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 32 3.2.3 A LINK BETWEEN THE CONTIGUITY MATRICES AND SPATIAL
CONFIGURA- TIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.4 LOCAL
S PATIAL S TRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 34 4 GAUSSIAN SPATIAL PROCESSES . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.1 BLENDING THE
DISTURBANCES WITH A S PATIAL S TRUCTURE . . . . . . . . . . . . 37 4.1.1
THE INTERNAL COMPOSITION OF S TOCHASTIC S PATIAL PROCESSES . . . . . . .
38 4.1.2 CONSTRAINING ASSUMPTIONS ON S PATIAL S TOCHASTIC PROCESSES . .
. . . . 40 4.1.3 EXCURSION: NON-HIERARCHICAL AGGREGATION OF S PATIAL
OBJECTS . . . . 41 4.2 DEFINITION AND PROPERTIES OF GAUSSIAN S PATIAL
PROCESSES . . . . . . . . 42 4.2.1 THE AUTOREGRESSIVE S PATIAL PROCESS .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.2 THE
MOVING AVERAGE PROCESS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 46 4.2.3 EXCURSION: THE COMMON FACTOR CONSTRAINT AND
THE SPATIAL LAG MODEL . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.3
TESTING FOR GAUSSIAN S PATIAL PROCESSES . . . . . . . . . . . . . . . .
. . . . . . . . . 47 4.3.1 TEST PRINCIPLES FOR SPATIAL AUTOCORRELATION
IN REGRESSION RESIDUALS 49 4.3.2 STATISTICAL PROPERTIES OF THE MORAN*S I
TEST . . . . . . . . . . . . . . . . . . . . 51 XII TABLE OF CONTENTS II
DEVELOPMENT AND PROPERTIES OF MORAN*S I *S DISTRIBUTION 5 THE
CHARACTERISTIC FUNCTION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 59 5.1 GENERAL PROPERTIES OF THE CHARACTERISTIC FUNCTION .
. . . . . . . . . . . . . 59 5.2 THE INVERSION THEOREM . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3
DISTRIBUTION OF A WEIGHTED SUM OF * 2 -DISTRIBUTED VARIABLES . . . . 63
5.4 EXTENSIONS AND COMMENTS . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 66 6 NUMERICAL EVALUATION OF IMHOF*S FORMULA
. . . . . . . . . . . . . . 67 6.1 INFLUENTIAL WEIGHTS IN IMHOF*S
FORMULA . . . . . . . . . . . . . . . . . . . . . . . . 67 6.2 A
NUMERICAL EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 67 6.3 THE BEHAVIOR OF THE INTEGRAND AT THE
ORIGIN . . . . . . . . . . . . . . . . . . . 68 6.4 DERIVATION OF AN
UPPER TRUNCATION POINT . . . . . . . . . . . . . . . . . . . . . . 69
6.5 NUMERICAL ALGORITHMS TO APPROXIMATE IMHOF*S FORMULA . . . . . . . .
70 6.5.1 EQUALLY S PACED S TEP-S IZE . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 71 6.5.2 VARIABLE S PACED S TEP-S
IZE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 72 7 THE EXACT DISTRIBUTION OF MORAN*S I . . . . . . . . . . . . .
. . . . . . . 75 7.1 DERIVATION OF THE DISTRIBUTION UNDER THE INFLUENCE
OF A SPATIAL PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 7.1.1
TRANSFORMATION INTO INDEPENDENT RANDOM VARIABLES . . . . . . . . . . . .
76 7.1.2 TRANSFORMATION OF MORAN*S I INTO A S IMPLE QUADRATIC FORM . . .
. . 77 7.1.3 DETERMINATION OF THE WEIGHTS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 77 7.1.4 DISCUSSION . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 78 7.2 SIMPLIFICATIONS UNDER THE ASSUMPTION OF SPATIAL
INDEPENDENCE . . 79 7.2.1 INDEPENDENCE OF THE EIGENVALUE SPECTRUM FROM
THE DENOMINATOR 80 7.2.2 SHIFTS IN THE EIGENVALUE SPECTRUM IN DEPENDENCE
OF MORAN*S I *S OBSERVED VALUE . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.2.3 BOUNDING
DISTRIBUTIONS OF MORAN*S I TO OBTAIN INDEPENDENCE FROM THE PROJECTION
MATRIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 83 8 THE SHAPE OF MORAN*S I EXACT DISTRIBUTION . . . . . . . . . .
. 89 8.1 THE FEASIBLE RANGE OF MORAN*S I . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 89 8.2 SPECIFIC EIGENVALUE SPECTRA AND
MORAN*S I *S DISTRIBUTION . . . . . . . 90 8.2.1 S MALL IRREGULAR S
PATIAL TESSELLATIONS . . . . . . . . . . . . . . . . . . . . . . . . . .
. 91 8.2.2 LARGE REGULAR S PATIAL TESSELLATIONS . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 93 9 THE MOMENTS OF MORAN*S I . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 99 9.1 THE MOMENTS
UNDER THE ASSUMPTION OF SPATIAL INDEPENDENCE . . . 99 9.1.1 THE THEOREM
BY PITMAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 99 9.1.2 THE EXPECTATIONS OF MORAN*S I NUMERATOR AND
DENOMINATOR . . . 100 9.1.3 EIGENVALUE OR TRACE EXPRESSIONS FOR THE
CENTRAL MOMENTS . . . . . . 101 9.2 THE CONDITIONAL MOMENTS OF MORAN*S I
. . . . . . . . . . . . . . . . . . . . . . . . 102 9.3 CORRELATION
BETWEEN DIFFERENT S PATIAL S TRUCTURES . . . . . . . . . . . . . . . 105
9.4 SOME APPLICATIONS USING MORAN*S I *S THEORETICAL MOMENTS . . . . .
106 TABLE OF CONTENTS XIII 9.4.1 APPROXIMATIONS OF MORAN*S I *S
DISTRIBUTION BY ITS MOMENTS . . . . 106 9.4.2 POTENTIAL APPLICATIONS OF
MORAN*S I *S CONDITIONAL EXPECTATION . . 108 III AN EMPIRICAL
APPLICATION OF MORAN*S I *S EXACT CONDITIONAL DISTRIBUTION 10 THE BASIC
ECOLOGICAL MODEL AND SPATIAL SETTING . . . . . . 117 10.1 THE S ETTING
OF THE REGRESSION MODEL . . . . . . . . . . . . . . . . . . . . . . . .
. . . 118 10.2 THE S PATIAL S ETTING . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 122 10.2.1 RATIONALE
FOR AN UNDERLYING SPATIAL PROCESS IN DISEASE RATES . . . 123 10.2.2
APPROXIMATION OF A HIERARCHICAL MIGRATORY GRAPH . . . . . . . . . . . .
. . 124 10.2.3 TESTING FOR INHERENT S PATIAL AUTOCORRELATION . . . . . .
. . . . . . . . . . . . . 128 11 A SPATIAL ANALYSIS OF THE CANCER DATA .
. . . . . . . . . . . . . . . . . 129 11.1 LINKING MORAN*S I TO AN
AUTOREGRESSIVE S PATIAL PROCESS . . . . . . . . 129 11.2 EXPLORATORY
ANALYSIS BY MEANS OF LOCAL MORAN*S I I , . . . . . . . . . . . . 131
11.2.1 LOCAL MORAN*S I I AS RATIO OF QUADRATIC FORMS . . . . . . . . . .
. . . . . . . 132 11.2.2 THE CONDITIONAL DISTRIBUTION OF LOCAL MORAN*S I
I , . . . . . . . . . . . . . . 133 11.2.3 CORRELATION BETWEEN LOCAL
MORAN*S I I . . . . . . . . . . . . . . . . . . . . . . . . . . 136
11.2.4 IMPACT OF THE LOCAL REGRESSION RESIDUALS . . . . . . . . . . . .
. . . . . . . . . . 138 11.3 THE IDENTIFICATION OF A PREVAILING SPATIAL
PROCESS . . . . . . . . . . . . . . . 140 11.3.1 THE POWER FUNCTION OF
GLOBAL MORAN*S I . . . . . . . . . . . . . . . . . . . . . . 141 11.3.2
IDENTIFICATION OF A S PATIAL PROCESS BY A NON-NESTED TEST . . . . . . .
. 142 11.4 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 144 12 CONCLUSIONS
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 147 REFERENCES . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 153 INDEX . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
163
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| any_adam_object | 1 |
| author | Tiefelsdorf, Michael 1958- |
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| author_facet | Tiefelsdorf, Michael 1958- |
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| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)614201546 (DE-599)BVBBV012782143 |
| discipline | Mathematik Geographie |
| format | Book |
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| id | DE-604.BV012782143 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:33:35Z |
| institution | BVB |
| isbn | 3540662081 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008693486 |
| oclc_num | 614201546 |
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| owner_facet | DE-355 DE-BY-UBR DE-12 DE-824 DE-91G DE-BY-TUM DE-706 DE-521 DE-83 DE-11 DE-188 |
| physical | XVIII, 167 S. graph. Darst., Kt. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in earth sciences |
| series2 | Lecture notes in earth sciences |
| spelling | Tiefelsdorf, Michael 1958- Verfasser (DE-588)12131328X aut Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables Michael Tiefelsdorf Berlin [u.a.] Springer 2000 XVIII, 167 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Lecture notes in earth sciences 87 Räumliche Differenzierung (DE-588)4115688-2 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Räumliche Differenzierung (DE-588)4115688-2 s DE-604 Räumliche Statistik (DE-588)4386767-4 s Lecture notes in earth sciences 87 (DE-604)BV023550940 87 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693486&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tiefelsdorf, Michael 1958- Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables Lecture notes in earth sciences Räumliche Differenzierung (DE-588)4115688-2 gnd Räumliche Statistik (DE-588)4386767-4 gnd |
| subject_GND | (DE-588)4115688-2 (DE-588)4386767-4 |
| title | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables |
| title_auth | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables |
| title_exact_search | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables |
| title_full | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables Michael Tiefelsdorf |
| title_fullStr | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables Michael Tiefelsdorf |
| title_full_unstemmed | Modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables Michael Tiefelsdorf |
| title_short | Modelling spatial processes |
| title_sort | modelling spatial processes the identification and analysis of spatial relationships in regression residuals by means of moran s i with 8 tables |
| title_sub | the identification and analysis of spatial relationships in regression residuals by means of Moran's I ; with 8 tables |
| topic | Räumliche Differenzierung (DE-588)4115688-2 gnd Räumliche Statistik (DE-588)4386767-4 gnd |
| topic_facet | Räumliche Differenzierung Räumliche Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008693486&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023550940 |
| work_keys_str_mv | AT tiefelsdorfmichael modellingspatialprocessestheidentificationandanalysisofspatialrelationshipsinregressionresidualsbymeansofmoransiwith8tables |