Type: Package
Title: Compare Models with Cross-Validated Log-Likelihood
Version: 1.0.4
Date: 2022-05-04
Author: Shana Scogin <shanarscogin@gmail.com>, Sarah Petersen <sarahllpetersen@gmail.com>, Jeff Harden <jeff.harden@nd.edu>, Bruce A. Desmarais <bdesmarais@psu.edu>
Maintainer: Shana Scogin <shanarscogin@gmail.com>
Description: An implementation of the cross-validated difference in means (CVDM) test by Desmarais and Harden (2014) <doi:10.1007/s11135-013-9884-7> (see also Harden and Desmarais, 2011 <doi:10.1177/1532440011408929>) and the cross-validated median fit (CVMF) test by Desmarais and Harden (2012) <doi:10.1093/pan/mpr042>. These tests use leave-one-out cross-validated log-likelihoods to assist in selecting among model estimations. You can also utilize data from Golder (2010) <doi:10.1177/0010414009341714> and Joshi & Mason (2008) <doi:10.1177/0022343308096155> that are included to facilitate examples from real-world analysis.
URL: https://github.com/ShanaScogin/modeLLtest
License: GPL-3
NeedsCompilation: yes
BugReports: https://github.com/ShanaScogin/modeLLtest/issues
Imports: stats, quantreg, survival, coxrobust, MASS, Rcpp
Depends: R (≥ 3.2.3)
Encoding: UTF-8
LazyData: TRUE
LazyLoad: TRUE
Suggests: knitr, rmarkdown, testthat
VignetteBuilder: knitr
SystemRequirements: GNU make
RoxygenNote: 7.1.2
LinkingTo: Rcpp, RcppArmadillo
Packaged: 2022-05-05 20:36:55 UTC; shanascogin
Repository: CRAN
Date/Publication: 2022-05-05 23:20:17 UTC

Cross-Validated Difference in Means (CVDM) Test

Description

Applies cross-validated log-likelihood difference in means test to compare two methods of estimating a formula. The output identifies the more appropriate model.

In choosing between OLS and MR, please cite:

For other applications of the CVDM test, please cite:

Usage

cvdm(
  formula,
  data,
  method1 = c("OLS", "MR", "RLM", "RLM-MM"),
  method2 = c("OLS", "MR", "RLM", "RLM-MM"),
  subset,
  na.action,
  ...
)

Arguments

formula

A formula object, with the dependent variable on the left of a ~ operator, and the independent variables on the right.

data

A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.

method1

A method to estimate the model. Currently takes Ordinary Least Squares ("OLS"), Median Regression ("MR"), Robust Linear Regression ("RLM") using M-estimation, and Robust Linear Regression using MM-estimation ("RLM-MM"). The algorithm method used to compute the fit for the median regression is the modified version of the Barrodale and Roberts algorithm for l1-regression, which is the rq default by R package quantreg. See quantreg rq function documentation for more details. Fitting for the robust regressions is done by iterated re-weighted least squares (IWLS) and is taken from the MASS package rlm function. The MM-estimation is the M-estimation with Tukey's biweight initialized by a specific S-estimate. The M-estimation, which can be achieved in this package with the option "RLM", is the default for the MASS rlm function. See MASS package rlm documentation for details.

method2

A method to estimate the model. Options are same as for method1.

subset

Expression indicating which subset of the rows of data should be used in the fit. All observations are included by default.

na.action

A missing-data filter function, applied to the model.frame, after any subset argument has been used.

...

Optional arguments, currently unsupported.

Details

This function implements the cross-validated difference in means (CVDM) test between two methods of estimating a formula. The function takes a formula and two methods and computes a vector of cross-validated log- likelihoods (CVLLs) for each method using the leave-one-out method. These output test score is the cross-validated Johnson's t-test. A positive test statistic supports the first method and a negative test statistic supports the second. Singular matrices during the leave-one-out cross-validation process are skipped.

Value

An object of class cvdm computed by the cross-validated log likelihood difference in means test (CVDM). The object is the Cross-Validated Johnson's t-test. A positive test statistic supports the first method and a negative test statistic supports the second. See cvdm_object for more details.

References

Examples



  set.seed(123456)
  b0 <- .2 # True value for the intercept
  b1 <- .5 # True value for the slope
  n <- 500 # Sample size
  X <- runif(n, -1, 1)

  Y <- b0 + b1 * X + rnorm(n, 0, 1) # N(0, 1 error)

  obj_cvdm <- cvdm(Y ~ X, data.frame(cbind(Y, X)), method1 = "OLS", method2 = "MR")

Cross-Validated Difference in Means (CVDM) Object

Description

This class of objects is returned by the cvdm function to compare two methods of estimating a formula.

Value

The following components must be included in a legitimate cvdm object.

best

name of the estimation method favored by the cvdm test.

test_stat

object returned by the bias-corrected Johnson's t-test. A positive test statistic supports method 1 and a negative test statistic supports method 2.

p_value

p-value for the test statistic.

n

number of observations.

df

degrees of freedom.

The object also contain the following: call, x, and y. See lm documentation for more.

See Also

cvdm

Cross-Validated Log Likelihood (CVLL)

Description

Extracts the leave-one-out cross-validated log-likelihoods from a method of estimating a formula.

Usage

cvll(
  formula,
  data,
  method = c("OLS", "MR", "RLM", "RLM-MM"),
  subset,
  na.action,
  ...
)

Arguments

formula

A formula object, with the dependent variable on the left of a ~ operator, and the independent variables on the right.

data

A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.

method

A method to estimate the model. Currently takes Ordinary Least Squares ("OLS"), Median Regression ("MR"), Robust Linear Regression ("RLM") using M-estimation, and Robust Linear Regression using MM-estimation ("RLM-MM"). The algorithm method used to compute the fit for the median regression is the modified version of the Barrodale and Roberts algorithm for l1-regression, which is the rq default by R package quantreg. See quantreg rq function documentation for more details. Fitting for the robust regressions is done by iterated re-weighted least squares (IWLS) and is taken from the MASS package rlm function. The MM-estimation is the M-estimation with Tukey's biweight initialized by a specific S-estimate. The M-estimation, which can be achieved in this package with the option "RLM", is the default for the MASS rlm function. See MASS package rlm documentation for details.

subset

Expression indicating which subset of the rows of data should be used in the fit. All observations are included by default.

na.action

A missing-data filter function, applied to the model.frame, after any subset argument has been used.

...

Optional arguments, currently unsupported.

Details

This function extracts a vector of leave-one-out cross-validated log likelihoods (CVLLs) from a method of estimating a formula. Singular matrices during the leave-one-out cross-validation process are skipped.

Value

An object of class cvll computed by the cross-validated log likelihood (CVLL). See cvdm_object for more details.

References

Examples



  set.seed(123456)
  b0 <- .2 # True value for the intercept
  b1 <- .5 # True value for the slope
  n <- 500 # Sample size
  X <- runif(n, -1, 1)

  Y <- b0 + b1 * X + rnorm(n, 0, 1) # N(0, 1 error)

  obj_cvll <- cvll(Y ~ X, data.frame(cbind(Y, X)), method = "OLS")

Cross-Validated Log-Likelihood (CVLL) Object

Description

This class of objects is returned by the cvll function.

Value

The following components must be included in a legitimate cvll object.

cvll

vector of cross-validated log-likelihood values using the leave-one-out method.

n

number of observations.

df

degrees of freedom.

method

method of estimation.

The object also contain the following: call, x, and y. See lm documentation for more.

See Also

cvll

Cross-Validated Difference in Means (CVDM) Test with Vector Imputs

Description

Applies cross-validated log-likelihood to test between two methods of estimating a formula. The output identifies the vector from the more appropriate model.

Please cite:

Desmarais, B. A., & Harden, J. J. (2014). An Unbiased Model Comparison Test Using Cross-Validation. Quality & Quantity, 48(4), 2155-2173. doi: 10.1007/s11135-013-9884-7

Usage

cvlldiff(vector1, vector2, df)

Arguments

vector1

A numeric vector of cross-validated log-likelihoods.

vector2

A numeric vector of cross-validated log-likelihoods.

df

A value of the degrees of freedom in the models.

Details

This function implements the cross-validated difference in means (CVDM) test between two vectors of cross-validated log-likelihoods. A positive test statistic supports the method that produced the first vector and a negative test statistic supports the second.

Value

An object of class cvlldiff computed by the cross-validated log likelihood difference in means test (CVDM). The test statistic object is the Cross-Validated Johnson's t-test. A positive test statistic supports the first method and a negative test statistic supports the second.See cvdm_object for more details.

References

Desmarais, B. A., & Harden, J. J. (2014). An Unbiased Model Comparison Test Using Cross-Validation. Quality & Quantity, 48(4), 2155-2173. doi: 10.1007/s11135-013-9884-7

Examples



  set.seed(123456)
  b0 <- .2 # True value for the intercept
  b1 <- .5 # True value for the slope
  n <- 500 # Sample size
  X <- runif(n, -1, 1)

  Y <- b0 + b1 * X + rnorm(n, 0, 1) # N(0, 1 error)
  cvll_ols <- cvll(Y ~ X, data.frame(cbind(Y, X)), method = "OLS")
  cvll_mr <- cvll(Y ~ X, data.frame(cbind(Y, X)), method = "MR")
  obj_compare <- cvlldiff(cvll_ols$cvll, cvll_mr$cvll, cvll_ols$df)

Cross-Validated Difference in Means (CVDM) Object from General cvlldiff Function

Description

This class of objects is returned by the cvlldiff function to compare vectors of cross-validated log-likelihood values.

Value

The following components must be included in a legitimate cvlldiff object.

best

name of the estimation method favored by the cvdm test.

test_stat

object returned by the bias-corrected Johnson's t-test. A positive test statistic supports the method that generated the first vector of cross-validated log-likelihood values and a negative test statistic supports the method that generated the second vector.

p_value

p-value for the test statistic.

See Also

cvlldiff

Cross-Validated Median Fit (CVMF) Test

Description

Applies cross-validated log-likelihood to test between partial likelihood maximization (PLM) and the iteratively reweighted robust (IRR) method of estimation for a given application of the Cox model. For more, see: Desmarais, B. A., & Harden, J. J. (2012). Comparing partial likelihood and robust estimation methods for the Cox regression model. Political Analysis, 20(1), 113-135. doi: 10.1093/pan/mpr042

Usage

cvmf(
  formula,
  data,
  method = c("exact", "approximate", "efron", "breslow"),
  trunc = 0.95,
  subset,
  na.action,
  f.weight = c("linear", "quadratic", "exponential"),
  weights,
  singular.ok = TRUE
)

Arguments

formula

A formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function from the survival package.

data

A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model or in the subset and the weights argument.

method

A character string specifying the method for tie handling in coxph(). If there are no tied death times all the methods are equivalent. Following the coxph function in the survival package, the Efron approximation is used as the default. The survival package justifies this due to the Efron method being is more accurate when dealing with tied death times, and is as efficient computationally than the common Breslow method. The "exact partial likelihood" is equivalent to a 'conditional logistic model, and is appropriate when the times are a small set of discrete values. This argument does not exist in the coxr function in the coxrobust package. For coxr, method is based on a smooth modification of the partial likelihood. See documentation from survival package for more on coxph method and coxrobust package for coxr method.

trunc

A value that determines the trimming level for the robust estimator. The default is 0.95. Roughly, quantile of the sample T_i exp(\beta'Z_i). It is an argument in the coxr function in the coxrobust package.

subset

Expression indicating which subset of the rows of data should be used in the fit. All observations are included by default.

na.action

A missing-data filter function, applied to the model.frame, after any subset argument has been used.

f.weight

A type of weighting function for coxr in the coxrobust package. The default is quadratic. See coxr documentation for more.

weights

A vector of case weights for coxph in the survival package. See coxph documentation for more.

singular.ok

Logical value indicating how to handle collinearity in the model matrix. If TRUE, the program will automatically skip over columns of the X matrix that are linear combinations of earlier columns. In this case the coefficients for such columns will be NA, and the variance matrix will contain zeros. For ancillary calculations, such as the linear predictor, the missing coefficients are treated as zeros.

Details

This function implements the cross-validated median fit (CVMF) test. The function cvmf() tests between the partial likelihood maximization (PLM) and the iteratively reweighted robust (IRR) method of estimation for a given application of the Cox model. The Cox model is a partial parametric model that does not make assumptions about the baseline hazard. It can be estimated via PLM, the standard estimator, or IRR, a robust estimator that identifies and downweights outliers. The choice between the two methods involves a trade-off between bias and efficiency. PLM is more efficient, but biased under specification problems. IRR reduces bias, but results in high variance due to the loss of efficiency. The cvmf() function returns an object to identify the prefered estimation method.

See also coxph, coxr, Surv

Value

An object of class cvmf computed by the cross-validated median fit test (CVMF) to test between the PLM and IRR methods of estimating the Cox model. See cvmf_object for more details.

References

Desmarais, B. A., & Harden, J. J. (2012). Comparing partial likelihood and robust estimation methods for the Cox regression model. Political Analysis, 20(1), 113-135. doi: 10.1093/pan/mpr042

Examples



  set.seed(12345)
  x1 <- rnorm(100)
  x2 <- rnorm(100)

  x2e <- x2 + rnorm(100, 0, 0.5)

  y <- rexp(100, exp(x1 + x2))
  y <- survival::Surv(y)

  dat <- data.frame(y, x1, x2e)
  form <- y ~ x1 + x2e

  results <- cvmf(formula = form, data = dat)

Cross-Validated Median Fit (CVMF) Object

Description

This class of objects is returned by the cvmf function to test between the partial likelihood maximization (PLM) and the iteratively reweighted robust (IRR) method of estimation for a given application of the Cox model.

Value

The following components must be included in a legitimate cvmf object.

best

name of the model of estimation favored by the cvmf test.

p

p-value of the binomial test used to test between estimation models.

cvmf

full output of the binomial test used to test between estimation methods. See documentation for binom.test for more information.

coef_names

names of the coefficients.

irr

full output for the iteratively reweighted robust (IRR) method of estimating the Cox model. See documentation for coxr in the package coxrobust for more information.

plm

full output for the partial likelihood maximization (PLM) method of estimating the Cox model. See documentation for coxph in the package survival for more information.

irr_coefs

estimates obtained from IRR method of estimating the Cox model. See documentation for coxr in the package coxrobust for more information.

plm_coefs

estimates obtained from PLM method of estimating the Cox model. See documentation for coxph in the package survival for more information.

cvpl_irr

observation-wise contributions to the log-partial likelihood for IRR method of estimating the Cox model. See Desmarais and Hardin (Political Analysis 20:113-135, 2012) for more about the test and Verweij and Houwelingen (Statistics in Medicine 12(24): 2305–14, 1993) for more about the measure

cvpl_plm

observation-wise contributions to the log-partial likelihood for PLM method of estimating the Cox model. See Desmarais and Hardin (Political Analysis 20:113-135, 2012) for more about the test and Verweij and Houwelingen (Statistics in Medicine 12(24): 2305–14, 1993) for more about the measure

The object also contain the following: call, x, and y.

See Also

cvmf

Data from Golder (2010) on government formation in Western Europe

Description

Data from a study on Western European government formation duration. Data is at the country-level (N = 409). Variable names are taken directly from original dataset. The data is publicly available and has been included here with the endorsement of the author. Please see the original codebook for a more detailed description of the variables.

Usage

data(govtform)

Format

A data frame with 410 rows and 18 variables. The following are taken from the codebook at doi: 10.7910/DVN/BUWZBA.

countryname

names of countries used in analysis

country

unique number identifying each country

cabinet

unique number identifying each country. Begins with country code, followed by cabinets 1 - n

bargainingdays

the number of days between either an election or the resignation of the previous government and the day on which the new government is officially inaugurated

datein

date on which a government took office. Format is YYMMDD

dateout

date on which a government left office. Format is YYMMDD

postelection

dichotomous variable that equals 1 if a government is the first to form after an election (more uncertainty) and 0 if it forms in an interelection period (less uncertainty)

nonpartisan

dichotomous variable that equals 1 if the government is nonpartisan and 0 otherwise

legislative_parties

a fraction representing the number of parties that have won legislative seats. See codebook for more detail

inconclusive

the number of inconclusive bargaining rounds prior to a new government successfully forming

cabinetname

cabinet name identified by surname of prime minister (followed by a number if the PM presided over more than one cabinet)

singleparty_majority

dichotomous variable that equals 1 if a single party controls a majority of the legislative seats, 0 otherwise

polarization

measures the level of ideological polarization in the party system. See codebook for more detail

continuation

dichotomous variable that equals 1 if the outgoing government or formateur gets the first opportunity to form a new government, 0 otherwise. See codebook for more detail

positive_parl

dichotomous variable that equals 1 if a new government requires the explicit support of a legislative majority in order to take office, 0 otherwise. See codebook for more detail

post_legislative_parties

interaction term made by multiplying the postelection variable with the legislative_parties variable

post_polariz

interaction term made by multiplying the postelection variable with the polarization variable

post_positive

interaction term made by multiplying the postelection variable with the positive_parl variable

Source

doi: 10.7910/DVN/BUWZBA

References

Golder, S. N. (2010). Bargaining delays in the government formation process. Comparative Political Studies, 43(1), 3-32. doi: 10.1177/0010414009341714

Examples




data(govtform)

library(survival)
library(coxrobust)
library(modeLLtest)

# Survival models with data from Golder (2010)
golder_surv <- Surv(govtform$bargainingdays)
golder_x <- cbind(govtform$postelection, govtform$legislative_parties,
   govtform$polarization, govtform$positive_parl, govtform$post_legislative_parties,
   govtform$post_polariz, govtform$post_positive, govtform$continuation,
   govtform$singleparty_majority)
colnames(golder_x) <- c("govtform$postelection", "govtform$legislative_parties",
   "govtform$polarization", "govtform$positive_parl", "govtform$post_legislative_parties",
   "govtform$post_polariz", "govtform$post_positive", "govtform$continuation",
   "govtform$singleparty_majority")
golder_cox <- coxph(golder_surv ~ golder_x, method = "efron",
   data = govtform)
golder_robust <- coxr(golder_surv ~ golder_x, data = govtform)

# Comparing PLM to IRR methods of estimating the survival model
obj_cvmf_golder <- cvmf(golder_surv ~ golder_x, method = "efron",
   data = govtform)

obj_cvmf_golder

modeLLtest Overview

Description

modeLLtest has three main functions to implement cross validated log likelihood tests. To use this package, decide which specification(s) of a model and distributions you wish compare. The function cvdm() compares the fits of one model specification between a median regression and ordinary least squares. The function cvmf() compares between the fits of one model specification between two estimations of a Cox model. The function cvll() extracts the leave-one-out cross-validated log-likelihoods from a method of estimating a formula.

Data from Joshi and Mason (2008) on voter turnout in Nepal

Description

Data from a study on the relationship between land tenure and voter turnout in the three rounds of parliamentary elections in Nepal from the restoration of democracy in 1990 to 1999. Data is at the district-level (N = 75). Variable names are taken directly from original dataset. The data is publicly available and has been included here with the endorsement of the authors.

Usage

data(nepaldem)

Format

A data frame with 76 rows and 73 variables:

sn

a column of identifiers. This column is not a variable

district

names of the district in Nepal used in analysis

householdsize

average size of household in district

total_holding

total land holding

noown_single_tenure

number of households that own and cultivate land under single tenure

norent_single_ten

number of households that rent for service and cultivate land under single tenure

noother_single_ten

number of households that cultivate under single tenure and have another set up other than those above

nomore1_ten_hold

number of households with more than one tenure

noholding_below1_pa

number of households that hold less than 1.0 hectares of land

noholding_2to3_pa

number of households that hold 2 to 3 hectares of land

noholding_4to5_pa

number of households that hold 4 to 5 hectares of land

noholding_6to9_pa

number of households that hold 6 to 9 hectares of land

noholding_10_pa

number of households with more than 10 parcels of land

total_ha

total hectares of land

total_parcel

total parcels of land

no_hold_fixmoney2

subsection of number of households with fixed cash rent

no_hold_fixproduct2

subsection of households with fixed product rent

no_hold_share2

subsection of households participating in sharecropping

no_hold_services2

subsection of households participating in sharecropping

no_hold_mortgage2

subsection of households with a mortgage

no_hold_fixmoney1

subsection of households with fixed cash rent

no_hold_fixproduct1

subsection of households with fixed product rent

no_hold_share1

subsection of households participating in sharecropping

no_hold_services1

subsection of households with rent for service

no_hold_mortgage1

subsection of households with a mortgage

totalhouseholds

total number of households

landless

number of landless households

totalvoters1991

total number of voters in 1991

totalcastedvote1991

total number of votes cast in 1991

totalvalidvote1991

total number of valid votes in 1991

constituency1991

constituency in 1991

totalcontestants1991

total number of candidates contesting elections in 1991

totalvoters1994

total number of voters in 1994

totalcastedvote1994

total number of votes cast in 1994

totalvalidvote1994

total number of valid votes in 1994

constituency1994

constituency in 1994

totalcontestants1994

total number of candidates contesting elections in 1994

togalvoters1999

total number of voters in 1999

totalcastedvote1999

total number of votes cast in 1999

totalvalidvote1999

total number of valid votes in 1999

constituency1999

constituency in 1999

totalcontestants1999

total number of candidates contesting elections in 1999

pop_2001

population in 2001

hdi_1996

HDI 1996 (index 0 to 1)

per_without_instcredit

percent without access to institutional credit

access_instutional_credit

access to institutional credit

total_hh_sharecrop

total number of households participating in sharecropping

total_hh_fixmoney

total number of households with fixed cash rent

total_hh_fixproduct

total number of households with fixed product rent

total_hh_service

total number of households with rent for service

total_hh_mortgage

total number of households with a mortgage

total_killed

total number of people killed. This serves as a measure of political violence during the insurgency

percent_regvote1991

election turnout for 1991 as measured by the percentage of registered voters who voted in the national parliamentary election

percent_regvote1994

election turnout for 1994 as measured by the percentage of registered voters who voted in the national parliamentary election

percent_regvote1999

election turnout for 1999 as measured by the percentage of registered voters who voted in the national parlimentary election

per_total_hold_sharecrop

percent of sharecropping households

per_total_hold_fixmoney

percent of households that have a fixed cash rent

per_total_hold_fixproduct

percent of households that have a fixed product rent

per_total_hold_service

percent of households that have rent for service

per_total_hold_mortgage

percent of households with a mortgage

per_noholding_below1_pa
landless_1000

landless households (in 1,000s)

totoalkilled_1000

total number of people killed (in 1,000s). This serves as a measure of political violence during the insurgency

cast_eth_fract

caste and ethnic fractionalization

languistic_fract

linguistic fractionalization

landless_gap

landless households (in 1,000s) gap

below1pa_gap

percent smallholder households gap

sharecrop_gap

percent sharecropping households gap

service_gap

percent rent for service households gap

fixmoney_gap

percent fixed cash rent households gap

fixprod_gap

percent fixed product rent households gap

hdi_gap

HDI 1996 (index 0 to 1) gap

ln_pop2001

population in 2001 (logged)

hdi_gap1

HDI 1996 (index 0 to 1) gap (positive values)

Source

Journal of Peace Research Replication Datasets

References

Joshi, M., & Mason, T. D. (2008). Between democracy and revolution: peasant support for insurgency versus democracy in Nepal. Journal of Peace Research, 45(6), 765-782. doi: 10.1177/0022343308096155

Examples



data(nepaldem)

library(MASS)
library(modeLLtest)

# Models from Joshi and Mason (2008)
model_1991 <- rlm(percent_regvote1991 ~ landless_gap +
   below1pa_gap + sharecrop_gap + service_gap + fixmoney_gap +
   fixprod_gap + per_without_instcredit + hdi_gap1 + ln_pop2001 +
   totalcontestants1991 + cast_eth_fract, data = nepaldem)

model_1994 <- rlm(percent_regvote1994 ~ landless_gap +
   below1pa_gap + sharecrop_gap + service_gap + fixmoney_gap +
   fixprod_gap +  per_without_instcredit + hdi_gap1 + ln_pop2001 +
   totalcontestants1994 + cast_eth_fract, data = nepaldem)

model_1999a <- rlm(percent_regvote1999 ~ landless_gap +
   below1pa_gap + sharecrop_gap + service_gap + fixmoney_gap +
   fixprod_gap + per_without_instcredit + hdi_gap1 + ln_pop2001 +
   totalcontestants1999 + cast_eth_fract, data = nepaldem)

model_1999b <- rlm(percent_regvote1999 ~ landless_gap +
   below1pa_gap + sharecrop_gap + service_gap + fixmoney_gap +
   fixprod_gap + per_without_instcredit + totoalkilled_1000 +
   hdi_gap1 + ln_pop2001 + totalcontestants1999 + cast_eth_fract,
   data = nepaldem)

# Comparing OLS to RR fit for model_1999b
obj_cvdm_jm <- cvdm(percent_regvote1999 ~ landless_gap +
   below1pa_gap + sharecrop_gap + service_gap + fixmoney_gap +
   fixprod_gap + per_without_instcredit + totoalkilled_1000 +
   hdi_gap1 + ln_pop2001 + totalcontestants1999 + cast_eth_fract,
   data = nepaldem, method1 = "OLS", method2 = "RLM-MM")

obj_cvdm_jm