On the Identification of Trend and Correlation in Temporal and Spatial Regression View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2008

AUTHORS

Ludwig Fahrmeir , Thomas Kneib

ABSTRACT

In longitudinal or spatial regression problems, estimation of temporal or spatial trends is often of primary interest, while correlation itself is of secondary interest or is regarded as a nuisance component. In other situations, the stochastic process inducing the correlation may be of interest in itself. In this paper, we investigate for some simple time series and spatial regression models, how well trend and correlation can be separated if both are modeled in a flexible manner. In this contribution we shed some further light on this puzzle from a Bayesian perspective.We focus on approaches with Bayesian smoothing priors for modeling trend functions, such as random walk models or extensions to Bayesian penalized (P-)splines. If the correlation-generating error process has similar stochastic structure as the smoothing prior it seems quite plausible that identi.ability problems can arise. In particular, it can become difficult to separate trend from correlation. We first exemplify this using a simple time series setting in Section 2. In Section 3 we move on to the corresponding spatial situation, which arises in geostatistics. Section 4 brie.y points out extensions to the general class of structured additive regression (STAR) models. More... »

PAGES

1-27

References to SciGraph publications

Book

TITLE

Recent Advances in Linear Models and Related Areas

ISBN

978-3-7908-2063-8
978-3-7908-2064-5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-7908-2064-5_1

DOI

http://dx.doi.org/10.1007/978-3-7908-2064-5_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1026090526


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Ludwig Maximilian University of Munich", 
          "id": "https://www.grid.ac/institutes/grid.5252.0", 
          "name": [
            "Department of Statistics, University of Munich, Ludwigstrasse 33, 80539, Munich, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fahrmeir", 
        "givenName": "Ludwig", 
        "id": "sg:person.0661512671.36", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0661512671.36"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Ludwig Maximilian University of Munich", 
          "id": "https://www.grid.ac/institutes/grid.5252.0", 
          "name": [
            "Department of Statistics, University of Munich, Ludwigstrasse 33, 80539, Munich, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kneib", 
        "givenName": "Thomas", 
        "id": "sg:person.01272020411.15", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01272020411.15"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.csda.2004.10.011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1015498897"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1030637857", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-3454-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030637857", 
          "https://doi.org/10.1007/978-1-4757-3454-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4757-3454-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030637857", 
          "https://doi.org/10.1007/978-1-4757-3454-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/9781118150658.ch6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036775744"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-57348-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051599040", 
          "https://doi.org/10.1007/978-3-642-57348-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-57348-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051599040", 
          "https://doi.org/10.1007/978-3-642-57348-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-9076-1_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052474569", 
          "https://doi.org/10.1007/978-1-4419-9076-1_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-9076-1_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052474569", 
          "https://doi.org/10.1007/978-1-4419-9076-1_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/biomet/90.1.43", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059421269"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/016214502760047014", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064198007"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/016214507000000978", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064198712"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1198/1061860043010", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064199409"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2008", 
    "datePublishedReg": "2008-01-01", 
    "description": "In longitudinal or spatial regression problems, estimation of temporal or spatial trends is often of primary interest, while correlation itself is of secondary interest or is regarded as a nuisance component. In other situations, the stochastic process inducing the correlation may be of interest in itself. In this paper, we investigate for some simple time series and spatial regression models, how well trend and correlation can be separated if both are modeled in a flexible manner. In this contribution we shed some further light on this puzzle from a Bayesian perspective.We focus on approaches with Bayesian smoothing priors for modeling trend functions, such as random walk models or extensions to Bayesian penalized (P-)splines. If the correlation-generating error process has similar stochastic structure as the smoothing prior it seems quite plausible that identi.ability problems can arise. In particular, it can become difficult to separate trend from correlation. We first exemplify this using a simple time series setting in Section 2. In Section 3 we move on to the corresponding spatial situation, which arises in geostatistics. Section 4 brie.y points out extensions to the general class of structured additive regression (STAR) models.", 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-7908-2064-5_1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-7908-2063-8", 
        "978-3-7908-2064-5"
      ], 
      "name": "Recent Advances in Linear Models and Related Areas", 
      "type": "Book"
    }, 
    "name": "On the Identification of Trend and Correlation in Temporal and Spatial Regression", 
    "pagination": "1-27", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1026090526"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-7908-2064-5_1"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "7c4b06195dc2223fdd400fa485fe6ad4b853fd1ca8e1506298606ef33b0cf0df"
        ]
      }
    ], 
    "publisher": {
      "location": "Heidelberg", 
      "name": "Physica-Verlag HD", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-7908-2064-5_1", 
      "https://app.dimensions.ai/details/publication/pub.1026090526"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-16T07:26", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000355_0000000355/records_52987_00000000.jsonl", 
    "type": "Chapter", 
    "url": "https://link.springer.com/10.1007%2F978-3-7908-2064-5_1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-7908-2064-5_1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-7908-2064-5_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-7908-2064-5_1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-7908-2064-5_1'


 

This table displays all metadata directly associated to this object as RDF triples.

98 TRIPLES      22 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-7908-2064-5_1 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Ndd90632238ef44e1bd57c257556bfcaa
4 schema:citation sg:pub.10.1007/978-1-4419-9076-1_2
5 sg:pub.10.1007/978-1-4757-3454-6
6 sg:pub.10.1007/978-3-642-57348-4
7 https://app.dimensions.ai/details/publication/pub.1030637857
8 https://doi.org/10.1002/9781118150658.ch6
9 https://doi.org/10.1016/j.csda.2004.10.011
10 https://doi.org/10.1093/biomet/90.1.43
11 https://doi.org/10.1198/016214502760047014
12 https://doi.org/10.1198/016214507000000978
13 https://doi.org/10.1198/1061860043010
14 schema:datePublished 2008
15 schema:datePublishedReg 2008-01-01
16 schema:description In longitudinal or spatial regression problems, estimation of temporal or spatial trends is often of primary interest, while correlation itself is of secondary interest or is regarded as a nuisance component. In other situations, the stochastic process inducing the correlation may be of interest in itself. In this paper, we investigate for some simple time series and spatial regression models, how well trend and correlation can be separated if both are modeled in a flexible manner. In this contribution we shed some further light on this puzzle from a Bayesian perspective.We focus on approaches with Bayesian smoothing priors for modeling trend functions, such as random walk models or extensions to Bayesian penalized (P-)splines. If the correlation-generating error process has similar stochastic structure as the smoothing prior it seems quite plausible that identi.ability problems can arise. In particular, it can become difficult to separate trend from correlation. We first exemplify this using a simple time series setting in Section 2. In Section 3 we move on to the corresponding spatial situation, which arises in geostatistics. Section 4 brie.y points out extensions to the general class of structured additive regression (STAR) models.
17 schema:genre chapter
18 schema:inLanguage en
19 schema:isAccessibleForFree false
20 schema:isPartOf Na0ddde134df6407cba49c35cb963bcce
21 schema:name On the Identification of Trend and Correlation in Temporal and Spatial Regression
22 schema:pagination 1-27
23 schema:productId N586a2f29dd7e4c21a6593d94e7a56ecd
24 Nc11d6a7e6b1d472b9613f2bc8c2936a7
25 Ndbe3125178f944c7a951f3a8a26b5912
26 schema:publisher N806eaa7804f14503a5265fe6ab8f801a
27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026090526
28 https://doi.org/10.1007/978-3-7908-2064-5_1
29 schema:sdDatePublished 2019-04-16T07:26
30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
31 schema:sdPublisher Nb993b65317964d17a3d276b585c8984c
32 schema:url https://link.springer.com/10.1007%2F978-3-7908-2064-5_1
33 sgo:license sg:explorer/license/
34 sgo:sdDataset chapters
35 rdf:type schema:Chapter
36 N586a2f29dd7e4c21a6593d94e7a56ecd schema:name doi
37 schema:value 10.1007/978-3-7908-2064-5_1
38 rdf:type schema:PropertyValue
39 N806eaa7804f14503a5265fe6ab8f801a schema:location Heidelberg
40 schema:name Physica-Verlag HD
41 rdf:type schema:Organisation
42 Na0ddde134df6407cba49c35cb963bcce schema:isbn 978-3-7908-2063-8
43 978-3-7908-2064-5
44 schema:name Recent Advances in Linear Models and Related Areas
45 rdf:type schema:Book
46 Nb993b65317964d17a3d276b585c8984c schema:name Springer Nature - SN SciGraph project
47 rdf:type schema:Organization
48 Nc11d6a7e6b1d472b9613f2bc8c2936a7 schema:name readcube_id
49 schema:value 7c4b06195dc2223fdd400fa485fe6ad4b853fd1ca8e1506298606ef33b0cf0df
50 rdf:type schema:PropertyValue
51 Ndbe3125178f944c7a951f3a8a26b5912 schema:name dimensions_id
52 schema:value pub.1026090526
53 rdf:type schema:PropertyValue
54 Ndd90632238ef44e1bd57c257556bfcaa rdf:first sg:person.0661512671.36
55 rdf:rest Nfaf920f4489e48bfbb04d60278c83146
56 Nfaf920f4489e48bfbb04d60278c83146 rdf:first sg:person.01272020411.15
57 rdf:rest rdf:nil
58 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
59 schema:name Mathematical Sciences
60 rdf:type schema:DefinedTerm
61 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
62 schema:name Statistics
63 rdf:type schema:DefinedTerm
64 sg:person.01272020411.15 schema:affiliation https://www.grid.ac/institutes/grid.5252.0
65 schema:familyName Kneib
66 schema:givenName Thomas
67 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01272020411.15
68 rdf:type schema:Person
69 sg:person.0661512671.36 schema:affiliation https://www.grid.ac/institutes/grid.5252.0
70 schema:familyName Fahrmeir
71 schema:givenName Ludwig
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0661512671.36
73 rdf:type schema:Person
74 sg:pub.10.1007/978-1-4419-9076-1_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052474569
75 https://doi.org/10.1007/978-1-4419-9076-1_2
76 rdf:type schema:CreativeWork
77 sg:pub.10.1007/978-1-4757-3454-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030637857
78 https://doi.org/10.1007/978-1-4757-3454-6
79 rdf:type schema:CreativeWork
80 sg:pub.10.1007/978-3-642-57348-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051599040
81 https://doi.org/10.1007/978-3-642-57348-4
82 rdf:type schema:CreativeWork
83 https://app.dimensions.ai/details/publication/pub.1030637857 schema:CreativeWork
84 https://doi.org/10.1002/9781118150658.ch6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036775744
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1016/j.csda.2004.10.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015498897
87 rdf:type schema:CreativeWork
88 https://doi.org/10.1093/biomet/90.1.43 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059421269
89 rdf:type schema:CreativeWork
90 https://doi.org/10.1198/016214502760047014 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064198007
91 rdf:type schema:CreativeWork
92 https://doi.org/10.1198/016214507000000978 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064198712
93 rdf:type schema:CreativeWork
94 https://doi.org/10.1198/1061860043010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064199409
95 rdf:type schema:CreativeWork
96 https://www.grid.ac/institutes/grid.5252.0 schema:alternateName Ludwig Maximilian University of Munich
97 schema:name Department of Statistics, University of Munich, Ludwigstrasse 33, 80539, Munich, Germany
98 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...