Package spregime. March 12, 2012

Transcription

1 Title Tools for Spatial Regime Analysis Version Date Author Maintainer Package spregime March 12, 2012 A set of tools designed test to test for spatial heterogeneity characterized by groupwise differences associated with a set of underlying spatial regimes. Includes routines for testing the stability of global models, individual coefficients, and error variances. License GPL(>= 2) Depends R(>= ), spdep URL R topics documented: print.spchow print.spcoef print.spgwhet print.summary.spchow print.summary.spcoef spchow spcoef spgwhet spregime summary.spchow summary.spcoef vote Index 13 1

2 2 print.spcoef print.spchow Print Function for spchow Objects Prints the test results associated with a given spchow object. ## S3 method for class spchow print(x,...) x a spchow class object. None print.spcoef Print Function for spcoef Objects Prints the test results associated with a given spcoef object. ## S3 method for class spcoef print(x,...) x a spcoef class object. None

3 print.spgwhet 3 print.spgwhet Print Function for spgwhet Objects Prints the test results associated with a given spgwhet object. ## S3 method for class spgwhet print(x,...) x a spgwhet class object. None print.summary.spchow Print Function for summary.spchow Objects Prints the test results associated with a given summary.spchow object. ## S3 method for class summary.spchow print(x,...) x a summary.spchow class object. None

4 4 spchow print.summary.spcoef Print Function for summary.spcoef Objects Prints the test results associated with a given summary.spcoef object. ## S3 method for class summary.spcoef print(x,...) x a summary.spcoef class object. None spchow Chow Test for Spatial Heterogeneity Estimates the stability of a given model across a set of user-specified regimes. spchow(restrict, group, data = list(), partial = FALSE, = "lm", listw = NULL,...) restrict group data partial listw lm-style formula for the restricted regression. lm-style formula depicting only the variable used to identify regimes (i.e. no dependent variable needed). model data frame. a logical value indicating whether or not to include group-specific intercepts in the restricted model. Default is FALSE. string indicating the type of model to use. lm indicates a non-spatial Chow test while lagsarlm and errorsarlm indicate alternative versions of a spatial Chow test. The default is lm. a listw object. The default value is NULL.... additional arguments to be passed to the model-fitting routine.

5 spchow 5 Details spchow compares the fit of a restricted or global model in which a given set of coefficients are treated as fixed to the fit of an unrestricted or local model in which the coefficients in question are allowed to vary across a set of user-specified regimes. Regime models are specified using two formulas, the first of which depicts the global model, the second of which depicts the variable used to specify regimes. Spatial regime models are estimated using the errorsarlm and lagsarlm routines available as part of the spdep package. The resulting test is ultimately carried out using the anova command which, in the case of non-spatial regime models, results in the standard F- test. In contrast, the use of the anova command in the context of likelihood-based models such as errorsarlm and lagsarlm results in a likelihood ratio test. The null model can be adjusted to allow for regime-specific intercepts. A spchow object containing the following elements: call the call used to create this object. either "lm", "errorsarlm", or "lagsarlm". base.terms the coefficients associated with the restricted model. regime.variable the variable used to define regimes. regime.labels res.formula unres.formula res.mod unres.mod res.resdf unres.resdf chow the vector of regime names associated with regime.variable. a symbolic description of the restricted model. a symbolic description of the unrestricted model. the results of the restricted model. the results of the unrestricted model. the residual degrees of freedom for the restricted model. the residual degrees of freedom for the unrestricted model. the results of the ANOVA-based test comparing the restricted and unrestricted models. References Anselin, L Spatial Econometrics: Methods and Models. Durdrecht: Kluwer Academic Publishers, pp Chow, G "Tests of Equality Between Sets of Coefficients in Two Linear Regressions." Econometrica 28: Examples data(vote1890, package = "spregime") #Spatial Chow chow<-spchow(restrict = VOTE~WHEAT+DAIRY+TENANT+GERMAN+SCAND, group = ~STATE, data = vote1890, = "lagsarlm", listw = vote.wgts) chow

6 6 spcoef spcoef Regime-Based Tests for Coefficient Stability Tests the stability of individual coefficients across a set of user-defined regimes. spcoef(restrict, group, data = list(), partial = FALSE, = "lm", listw = NULL,...) restrict group data Details partial listw lm-style formula for the restricted regression. lm-style formula depicting only the variable used to identify regimes (i.e. no dependent variable needed). model data frame. a logical value indicating whether or not to include group-specific intercepts in the restricted model. Default is FALSE. string indicating the type of model to use. lm indicates a non-spatial Chow test while lagsarlm and errorsarlm indicate alternative versions of a spatial Chow test. The default is lm. a listw object. The default value is NULL.... additional arguments to be passed to the model-fitting routine. spcoef compares the fit of a restricted or global model in which a given set of coefficients are treated as fixed to the fit of a series of unrestricted or local models in which a single coefficient is allowed to vary across a set of user-specified regimes. Regime models are specified using two formulas, the first of which depicts the global model, the second of which depicts the variable used to specify regimes. Spatial regime models are estimated using the errorsarlm and lagsarlm routines available as part of the spdep package. The resulting test is ultimately carried out using the anova command which, in the case of non-spatial regime models, results in the standard F- test. In contrast, the use of the anova command in the context of likelihood-based models such as errorsarlm and lagsarlm results in a likelihood ratio test. The null model can be adjusted to allow for regime-specific intercepts. Results for intercept-related models are suppressed when partial = TRUE. A spcoef object containing the following elements: call the call used to create this object. "lm", "errorsarlm", or "lagsarlm". base.terms the coefficients associated with the restricted model. regime.variable the variable used to define regimes.

7 spgwhet 7 regime.labels res.formula unres.formula res.mod unres.mod res.resdf unres.resdf test.vals the vector of regime names associated with regime.variable. a symbolic description of the restricted model. a list of symbolic descriptions associated with each of the unrestricted models. the results of the restricted model. a list of results associated with each of the unrestricted models. the residual degrees of freedom for the restricted model. a list of the residual degrees of freedom associated with each of the unrestricted models. a table summarizing the results of the ANOVA-based tests comparing the restricted and unrestricted models. Examples data(vote1890, package = "spregime") #Spatially-adjusted test for coefficient stability coefstab<-spcoef(restrict = VOTE~WHEAT+DAIRY+TENANT+GERMAN+SCAND, group = ~STATE, data = vote1890, partial = TRUE, = "lagsarlm", listw = vote.wgts) coefstab spgwhet Breusch-Pagan Test for Groupwise Heteroscedasticity Breusch-Pagan test for the equality of error variance across a set of user-defined regimes. spgwhet(restrict, group, data = list(), partial = FALSE, = "lm", listw = NULL, studentize = FALSE,...) restrict group data partial listw studentize lm-style formula for the restricted regression. lm-style formula depicting only the variable used to identify regimes (i.e. no dependent variable needed). model data frame. a logical value indicating whether or not to include group-specific intercepts in the restricted model. Default is FALSE. string indicating the type of model to use. lm indicates a non-spatial Chow test while lagsarlm and errorsarlm indicate alternative versions of a spatial Chow test. The default is lm. a listw object. The default value is NULL. a logical value indicating whether the residuals are studentized prior to inclusion in the auxiliary regression. Default is FALSE.... additional arguments to be passed to the model-fitting routine.

8 8 spregime Details spgwhet uses an auxiliary regression to test the null hypothesis that the variance in residuals associated with a restricted or global model is constant across a set of user-specified regimes. The test in question is specified using two formulas, the first of which depicts the restricted model, the second of which depicts the variable used to specify regimes and, hence, predict residual variance in the auxiliary regression. Spatially-adjusted residuals are introduced using the errorsarlm and lagsarlm routines available as part of the spdep package. The restricted model can be adjusted to allow for regime-specific intercepts. Residuals can be studentized to correct for non-normality, as per the work of Koenker (1981). A spgwhet object containing the following elements: call statistic parameter p.value method the call used to create this object. the value of the test statistic. degrees of freedom. the p-value associated with the test above. a character string indicating the type of test performed. References Anselin, L Spatial Econometrics: Methods and Models. Durdrecht: Kluwer Academic Publishers, pp Breusch, T. and A. Pagan "A Simple Test for Heteroscedasticity and Random Coefficient Variation." Econometrica 47: Koenker, R "A Note on Studentizing a Test for Heteroscedasticity." Econometrica 28: Examples data(vote1890, package = "spregime") #Spatially-adjusted BP test hettest<-spgwhet(restrict = VOTE~WHEAT+DAIRY+TENANT+GERMAN+SCAND, group = ~STATE, data = vote1890, = "lagsarlm", listw = vote.wgts) hettest spregime Tools for Spatial Regime Analysis A set of tools designed test to test for spatial heterogeneity characterized by groupwise differences associated with a set of underlying spatial regimes. Includes routines for testing the stability of global models, individual coefficients, and error variances.

9 summary.spchow 9 Details The spregime package contains a set of tools designed to replicate the types of regime analysis seen in works such as Baller et al. (2001) and Curtis et al. (2012). More specifically, the spchow routine estimates spatial and non-spatial Chow tests for the stability of coefficients across a set of userdefined regimes; the spcoef routine tests the stability of individual coefficients using both spatial and non-spatial models; and the spgwhet routine tests for groupwise heteroskedasticity. These routines have been designed to allow for partial tests in which expected outcomes in the null model are allowed to vary across regimes. References Anselin, L Spatial Econometrics: Methods and Models. Durdrecht: Kluwer Academic Publishers, pp Baller, R., L. Anselin, S. Messner, G. Deane, and D. Hawkins "Structural Covariates of U.S. County Homicide Rates: Incorporating Spatial Effects." Criminology 39: Curtis, K., P. Voss, and D. Long "Spatial Variation in Poverty-Generating Processes: Childhood Poverty in the United States." Social Science Research 41: summary.spchow Summary Statistics for spchow Objects Summarizes the results associated with a given spchow object. ## S3 method for class spchow summary(object,...) object a spchow class object.. A summary.spchow object containing the following elements: call res.formula unres.formula res.coef the call used to create the original spchow object. either "lm", "errorsarlm", or "lagsarlm". a symbolic description of the restricted model. a symbolic description of the unrestricted model. a matrix with columns representing the coefficients, standard errors, test statistics, and p-values associated with the restricted model.

10 10 summary.spcoef unres.coef res.sp unres.sp chow a set of regime-specific matrices with columns representing the coefficients, standard errors, test statistics, and p-values associated with the unrestricted model. the spatial coefficient associated with the restricted model. NULL in the case of lm objects. the spatial coefficient associated with the unrestricted model. NULL in the case of lm objects. the results of the ANOVA-based test comparing the restricted and unrestricted models. Examples data(vote1890, package = "spregime") #Spatial Chow chow<-spchow(restrict = VOTE~WHEAT+DAIRY+TENANT+GERMAN+SCAND, group = ~STATE, data = vote1890, = "lagsarlm", listw = vote.wgts) summary(chow) summary.spcoef Summary Statistics for spcoef Objects Summarizes the results associated with a given spcoef object. ## S3 method for class spcoef summary(object,...) object a spcoef class object.. A summary.spcoef object containing the following elements: call res.formula unres.formula res.coef unres.coef the call used to create the original spcoef object. either "lm", "errorsarlm", or "lagsarlm". a symbolic description of the restricted model. a list of symbolic descriptions associated with each of the unrestricted models. a matrix with columns representing the coefficients, standard errors, test statistics, and p-values associated with the restricted model. a set of variable-specific matrices with columns representing the coefficients, standard errors, test statistics, and p-values associated with the unrestricted model.

11 vote res.sp unres.sp test.vals the spatial coefficient associated with the restricted model. NULL in the case of lm objects. the set of spatial coefficients associated with each of the unrestricted models. NULL in the case of lm objects. a table summarizing the results of the ANOVA-based tests comparing the restricted and unrestricted models. Examples data(vote1890, package = "spregime") #Spatially-adjusted test for coefficient stability coefstab<-spcoef(restrict = VOTE~WHEAT+DAIRY+TENANT+GERMAN+SCAND, group = ~STATE, data = vote1890, = "lagsarlm", listw = vote.wgts) summary(coefstab) vote1890 Populist Voting on the Northern Great Plains, 1890 The dataset includes information on county-level election returns for gubernatorial contests in Minnesota, North Dakota, and South Dakota in 1890, along with information on select covariates drawn from the decennial census. data(vote1890) Format Data frame consisting of county-level voting and census data, along with geographic coordinates. NAME County name. STATE State name. FIPS1890 County FIPS code. X Horizontal position of county centroid in Cartesian coordinates. Y Vertical position of county centroid in Cartesian coordinates. VOTE The percentage of voters voting for a Populist gubernatorial candidate. WHEAT The percentage of improved acreage devoted to wheat production. DAIRY Thousands of gallons of milk per farm. TENANT Percentage of farms rented for money or crops. GERMAN Percentage of the population born in Germany. SCAND The percentage of the population born in Sweden, Norway, or Denmark.

12 12 vote1890 Details Source This columbus dataframe contains county-level voting and census data for 168 counties. Populist candidates are defined as candidates nominated by either the Alliance, Populist, or People s party. Independent candidates were also coded as Populist where appropriate (i.e. North Dakota in 1890 and South Dakota between 1890 and 1894). Data on Billings County, North Dakota were dropped due to having been excluded from the 1890 Census of Agriculture. vote.wgts is a listw object representing a first-order queen contiguity matrix. Haines, Michael R. and the Inter-University Consortium for Political and Social Research Historical, Demographic, Economic, and Social Data: The United States, [Computer file]. ICPSR02896-v2. Hamilton: Colgate University/Ann Arbor: Inter-University Consortium for Political and Social Research [producers]. Ann Arbor: Inter-University Consortium for Political and Social Research [distributor]. Inter-University Consortium for Political and Social Research United States Historical Election Returns, [Computer file]. ICPSR00001-v3. Ann Arbor: Inter-University Consortium for Political and Social Research [distributor], ,. doi: /ICPSR Examples data(vote1890, package = "spregime") plot(vote~wheat, data = vote1890) plot(vote.wgts, coords = cbind(vote1890$x, vote1890$y), col = red, lwd = 2)

13 Index Topic datasets vote1890, 11 print.spchow, 2 print.spcoef, 2 print.spgwhet, 3 print.summary.spchow, 3 print.summary.spcoef, 4 spchow, 4 spcoef, 6 spgwhet, 7 spregime, 8 summary.spchow, 9 summary.spcoef, 10 vote.wgts (vote1890), 11 vote1890, 11 13