Spatial Ordinary Least Squares (OLS)¶
공간 관계 진단을 포함하는 Ordinary Least Squares (OLS) 선형 회귀분석을 수행합니다.
Syntax
SpatialOLS (SimpleFeatureCollection inputFeatures, String dependentVariable, String explanatoryVariables, Boolean spatialDiagnotics, SpatialConcept spatialConcept, DistanceMethod distanceMethod, StandardizationMethod standardization, Double searchDistance ): SimpleFeatureCollection, SpatialOLSResult
Input Parameters
Identifier |
Description |
Type |
Default |
Required |
inputFeatures |
종속변수와 독립변수를 포함하고 있는 입력 레이어입니다. |
SimpleFeatureCollection |
✓ |
|
dependentVariable |
종속변수값을 가진 숫자 필드입니다. |
String |
✓ |
|
explanatoryVariables |
회귀 분석에 사용할 쉼표로 구분된 설명 변수 숫자 필드의 목록입니다. |
String |
✓ |
|
spatialDiagnotics |
Lagrange multiplier, Moran’s I 등 공간 진단을 포함할 지 여부를 설정합니다. |
Boolean |
✓ |
|
spatialConcept |
피처들 간에 공간 관계를 설정하는 방식을 선택합니다. |
SpatialConcept |
InverseDistance |
|
distanceMethod |
분석 대상 피처로부터 이웃 피처까지의 거리를 계산하는 방법을 설정합니다. |
DistanceMethod |
Euclidean |
|
standardization |
통계량 계산시 행 표준화 적용 여부를 설정합니다. |
StandardizationMethod |
None |
|
searchDistance |
역거리 혹은 고정 거리 옵션 선택 시 기준 값을 지정합니다. |
Double |
0.0 |
Process Outputs
Identifier |
Description |
Type |
Default |
Required |
olsFeatures |
종속 변수 추정치와 잔차를 포함한 출력 레이어입니다. |
SimpleFeatureCollection |
||
report |
OLS 분석 결과입니다. |
SpatialOLSResult |
✓ |
Constraints
Output은 XML로 반환한다.
Examples
a1_2000 필드를 종속변수로, a2_2000, a3_2000, a4_2000 필드를 설명변수로 분석한 결과는 다음의 XML 포맷으로 반환됩니다.
<?xml version="1.0" encoding="UTF-8"?>
<OrdinaryLeastSquares>
<ModelName>Ordinary Least Squares(OLS) Regression</ModelName>
<Dataset>seoul_series</Dataset>
<DependentVariable>a1_2000</DependentVariable>
<NumberOfObservations>25</NumberOfObservations>
<NumberOfVariables>4</NumberOfVariables>
<DegreesOfFreedom>21</DegreesOfFreedom>
<MeanDependentVar>18229.716524000003</MeanDependentVar>
<SdDependentVar>5222.973372203831</SdDependentVar>
<RSquared>0.2524024367985146</RSquared>
<AdjustedRSquared>0.14560278491258805</AdjustedRSquared>
<SumSquaredResidual>4.8945722348412424E8</SumSquaredResidual>
<SigmaSquare>2.3307486832577344E7</SigmaSquare>
<SeOfRegression>4827.782807104866</SeOfRegression>
<SigmaSquareML>1.957828893936497E7</SigmaSquareML>
<SeOfRegressionML>4424.736030472888</SeOfRegressionML>
<FStatistic>2.363326399800135</FStatistic>
<PValue>0.10015684828181148</PValue>
<LogLikelihood>-245.3476108684226</LogLikelihood>
<AIC>498.6952217368452</AIC>
<AICc>503.8531164736873</AICc>
<SchwarzCriterion>503.57072503631804</SchwarzCriterion>
<Summary>
<Variable>
<Variable>CONSTANT</Variable>
<Coefficient>-89839.01661165891</Coefficient>
<StandardError>45251.64301979817</StandardError>
<TStatistic>-1.9853205456507557</TStatistic>
<Probability>0.060320415845298396</Probability>
</Variable>
<Variable>
<Variable>a2_2000</Variable>
<Coefficient>1015.5016202521613</Coefficient>
<StandardError>459.27386712849943</StandardError>
<TStatistic>2.2111025532572612</TStatistic>
<Probability>0.03825397847242593</Probability>
</Variable>
<Variable>
<Variable>a3_2000</Variable>
<Coefficient>657.585445515956</Coefficient>
<StandardError>687.1537990129104</StandardError>
<TStatistic>0.9569698173255696</TStatistic>
<Probability>0.3494719862156815</Probability>
</Variable>
<Variable>
<Variable>a4_2000</Variable>
<Coefficient>74.91087027691356</Coefficient>
<StandardError>575.0254410828144</StandardError>
<TStatistic>0.13027401037396014</TStatistic>
<Probability>0.8975891001920921</Probability>
</Variable>
</Summary>
<VarianceInflationFactor>
<VIF>
<Variable>a2_2000</Variable>
<Value>1.0512492909076563</Value>
</VIF>
<VIF>
<Variable>a3_2000</Variable>
<Value>1.219785000060916</Value>
</VIF>
<VIF>
<Variable>a4_2000</Variable>
<Value>1.178277144719415</Value>
</VIF>
</VarianceInflationFactor>
<Multicollinearity>124.00930330161376</Multicollinearity>
<NormOfErrors>
<Diagnostics>
<Category>Test on Normality of Errors</Category>
<Name>Jarque-Bera</Name>
<DeegreesOfFreedom>2.0</DeegreesOfFreedom>
<Value>0.7273519517018467</Value>
<Probability>0.6951163927538146</Probability>
</Diagnostics>
</NormOfErrors>
<HrcDiagnostics>
<Diagnostics>
<Category>Diagnostics for Heteroskedasticity Random Coefficients</Category>
<Name>Breusch-Pagan</Name>
<DeegreesOfFreedom>3.0</DeegreesOfFreedom>
<Value>5.083212261808894</Value>
<Probability>0.16580435989410658</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Heteroskedasticity Random Coefficients</Category>
<Name>Koenker-Bassett</Name>
<DeegreesOfFreedom>3.0</DeegreesOfFreedom>
<Value>6.588607922676707</Value>
<Probability>0.08623276842110539</Probability>
</Diagnostics>
</HrcDiagnostics>
<SpatialDiagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Moran's I (error)</Name>
<DeegreesOfFreedom>-0.10552682243608924</DeegreesOfFreedom>
<Value>0.3551094963676925</Value>
<Probability>0.7225075633055715</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Lagrange Multiplier (lag)</Name>
<DeegreesOfFreedom>1.0</DeegreesOfFreedom>
<Value>0.3716414743314847</Value>
<Probability>0.5421108807877426</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Robust LM (lag)</Name>
<DeegreesOfFreedom>1.0</DeegreesOfFreedom>
<Value>0.09009324883412162</Value>
<Probability>0.5940365045566063</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Lagrange Multiplier (error)</Name>
<DeegreesOfFreedom>1.0</DeegreesOfFreedom>
<Value>0.5656327223255544</Value>
<Probability>0.4519995940481525</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Robust LM (error)</Name>
<DeegreesOfFreedom>1.0</DeegreesOfFreedom>
<Value>0.28408449682819137</Value>
<Probability>0.5940365045566063</Probability>
</Diagnostics>
<Diagnostics>
<Category>Diagnostics for Spatial Dependence</Category>
<Name>Lagrange Multiplier (SARMA)</Name>
<DeegreesOfFreedom>2.0</DeegreesOfFreedom>
<Value>0.655725971159676</Value>
<Probability>0.7204617265887313</Probability>
</Diagnostics>
</SpatialDiagnostics>
</OrdinaryLeastSquares>