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Linear Models with Replicate Weights

replm.Rd

Fits a linear model using lm for replicate weights. For a detailed explanation on how the standard errors are estimated see repse.

Usage

replm(
  formula,
  pvs = NULL,
  relatedpvs = TRUE,
  quiet = FALSE,
  summarize = TRUE,
  setup = NULL,
  df,
  wt,
  repwt,
  group = NULL,
  exclude = NULL,
  na.action = getOption("na.action"),
  method,
  aggregates = c("pooled", "composite")
)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

pvs

if plausible values are not used, this should be NULL. Otherwise it is a list indicating which variables from formula should be replaced by which plausible values variables. For more details check the examples.

relatedpvs

a logical value indicating if pvs are drawn from the same model. If TRUE (default), a total of \(n\) estimations will be done, where \(n\) is the number of plausible values for each plausible value variable. If FALSE, a total of \(n_1 \times n_2 \times n_...\) estimations will be done, where \(n_i\) is the number of plausible values in each plausible value variable.

quiet

a logical value indicating if progress status should be shown while estimating models by group. Default is FALSE.

summarize

a logical value indicating if lm objects should be converted to summary.lm or summary.glm objects and stripped from certain elements to reduce the size of the output object. Default is TRUE.

setup

an optional list produced by repsetup.

df

a data frame.

wt

a string specifying the name of the column (within df) with the total weights.

repwt

a string indicating the common names for the replicate weights columns (within df), or a data frame with the replicate weights.

group

a string specifying the variable name (within df) to be used for grouping. Categories in group are treated as independent, e.g., countries.

exclude

a vector indicating which groups (in the same format as group) should be excluded from the pooled and composite estimates.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

method

a string indicating the name of the replication method. Available options are: "JK2-full", "JK2-half", "FAY-0.5", and "JK2-half-1PV".

Additionally, ILSA names can be used, defaulting into:

  • "TIMSS", "PIRLS", or "LANA" for "JK2-full";

  • "ICILS", "ICCS", or "CIVED" for "JK2-half";

  • "PISA" or "TALIS" for "FAY-0.5";

  • and "oldTIMSS", "oldPIRLS", or "RLII" for "JK2-half-1PV".

Note that "oldTIMSS" and "oldPIRLS" refer to the method used for TIMSS and PIRLS before 2015, where within imputation variance is estimated using only 1 plausible value.

aggregates

a string vector indicating which aggregates should be included, options are "pooled" and "composite", both options can be used at the same time. If NULL no aggregate will be estimated.

Value

a list.

Examples

# Less data for shorter example
repdata2 <- repdata[1:1000,]

RW <- repcreate(df = repdata2, # the data frame with all the information
                 wt = "wt", # the total weights column name
                 jkzone = "jkzones", # the jkzones column name
                 jkrep = "jkrep", # the jkreps column name
                 repwtname = "REPWT", # the desired name for the rep weights
                 reps = 50, # the number of replications
                 method = "ICILS") # the name of the method aka the study name

### No groups ----

# Simple regression - weights within df
replm(formula = Math1 ~ 1 + GENDER,
      wt = "wt", # Name of total weight column within df
      repwt = "REPWT", # Common names of replicate weights within df
      df = cbind(repdata2,RW), # Data frame
      method = "ICILS") # the name of the method aka the study name
#> 50 weights found.
#> 51 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math1 ~ 1 + GENDER, df = cbind(repdata2, RW), 
#>     wt = "wt", repwt = "REPWT", method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.5270     0.0364  14.470        0
#> GENDER       -1.0007     0.0525 -19.055        0
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model:
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER, df = cbind(repdata2, RW), 
#>     wt = "wt", repwt = "REPWT", method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.52703    0.03995   13.19   <2e-16 ***
#> GENDER      -1.00073    0.05629  -17.78   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.09 on 998 degrees of freedom
#> Multiple R-squared:  0.2405,	Adjusted R-squared:  0.2398 
#> F-statistic: 316.1 on 1 and 998 DF,  p-value: < 2.2e-16
#> 

# Simple regression - weights as a separate data frame
replm(formula = Math1 ~ 1 + GENDER,
       wt = "wt", # Name of total weight column within df
       repwt = RW, # Data frame of weights
       df = repdata2, # Data frame
       method = "ICILS") # the name of the method aka the study name
#> 51 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math1 ~ 1 + GENDER, df = repdata2, wt = "wt", 
#>     repwt = RW, method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.5270     0.0364  14.470        0
#> GENDER       -1.0007     0.0525 -19.055        0
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model:
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER, df = repdata2, wt = "wt", 
#>     repwt = RW, method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.52703    0.03995   13.19   <2e-16 ***
#> GENDER      -1.00073    0.05629  -17.78   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.09 on 998 degrees of freedom
#> Multiple R-squared:  0.2405,	Adjusted R-squared:  0.2398 
#> F-statistic: 316.1 on 1 and 998 DF,  p-value: < 2.2e-16
#> 

# Multiple regression
replm(formula = Math1 ~ 1 + GENDER + Reading1,
       wt = "wt", # Name of total weight column within df
       repwt = RW, # Data frame of weights
       df = repdata2, # Data frame
       method = "ICILS") # the name of the method aka the study name
#> 51 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math1 ~ 1 + GENDER + Reading1, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.6057     0.0381  15.902        0
#> GENDER       -1.1401     0.0531 -21.473        0
#> Reading1      0.2532     0.0277   9.150        0
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model:
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER + Reading1, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.60574    0.03945  15.355   <2e-16 ***
#> GENDER      -1.14005    0.05638 -20.221   <2e-16 ***
#> Reading1     0.25321    0.02831   8.944   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.05 on 997 degrees of freedom
#> Multiple R-squared:  0.2969,	Adjusted R-squared:  0.2955 
#> F-statistic: 210.5 on 2 and 997 DF,  p-value: < 2.2e-16
#> 

# Multiple regression - with PVs
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading1, # Math1 now is "Math"
       wt = "wt", # Name of total weight column within df
       repwt = RW, # Data frame of weights
       df = repdata2, # Data frame
       pvs = pvs, # Named list
       method = "ICILS") # the name of the method aka the study name
#> 153 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math ~ 1 + GENDER + Reading1, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.6043     0.0381  15.863        0
#> GENDER       -1.1397     0.0571 -19.964        0
#> Reading1      0.3023     0.0575   5.259        0
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model for first plausible value combination:
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading1, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.60574    0.03945  15.355   <2e-16 ***
#> GENDER      -1.14005    0.05638 -20.221   <2e-16 ***
#> Reading1     0.25321    0.02831   8.944   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.05 on 997 degrees of freedom
#> Multiple R-squared:  0.2969,	Adjusted R-squared:  0.2955 
#> F-statistic: 210.5 on 2 and 997 DF,  p-value: < 2.2e-16
#> 

# Multiple regression - with more than one related PV variable
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3),
           Reading = paste0("Reading",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 
#> $Reading
#> [1] "Reading1" "Reading2" "Reading3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading, # Reading1 now is "Reading"
       wt = "wt", # Name of total weight column within df
       repwt = RW, # Data frame of weights
       df = repdata2, # Data frame
       pvs = pvs, # Named list
       method = "ICILS") # the name of the method aka the study name
#> 153 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.6512     0.0613  10.625    0.000
#> GENDER       -1.2266     0.1024 -11.983    0.000
#> Reading1      0.3501     0.1122   3.119    0.002
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model for first plausible value combination:
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.60574    0.03945  15.355   <2e-16 ***
#> GENDER      -1.14005    0.05638 -20.221   <2e-16 ***
#> Reading1     0.25321    0.02831   8.944   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.05 on 997 degrees of freedom
#> Multiple R-squared:  0.2969,	Adjusted R-squared:  0.2955 
#> F-statistic: 210.5 on 2 and 997 DF,  p-value: < 2.2e-16
#> 

# Multiple regression - with more than UNrelated PV variables
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3),
           Reading = paste0("Reading",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 
#> $Reading
#> [1] "Reading1" "Reading2" "Reading3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading, # Reading1 now is "Reading"
       wt = "wt", # Name of total weight column within df
       repwt = RW, # Data frame of weights
       df = repdata2, # Data frame
       pvs = pvs, # Named list
       relatedpvs = FALSE, # Unrelated PVs
       method = "ICILS") # the name of the method aka the study name
#> 459 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Replicate weights' model:
#>  
#> Call: 
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, relatedpvs = FALSE, 
#>     df = repdata2, wt = "wt", repwt = RW, method = "ICILS")
#> 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)   0.6575     0.0583  11.278        0
#> GENDER       -1.2378     0.0963 -12.858        0
#> Reading1      0.3687     0.0723   5.101        0
#> 
#> -------------------------------------------------------------------------------- 
#> Total weights' model for first plausible value combination:
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, relatedpvs = FALSE, 
#>     df = repdata2, wt = "wt", repwt = RW, method = "ICILS")
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#>     NA     NA     NA     NA     NA 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.60574    0.03945  15.355   <2e-16 ***
#> GENDER      -1.14005    0.05638 -20.221   <2e-16 ***
#> Reading1     0.25321    0.02831   8.944   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 1.05 on 997 degrees of freedom
#> Multiple R-squared:  0.2969,	Adjusted R-squared:  0.2955 
#> F-statistic: 210.5 on 2 and 997 DF,  p-value: < 2.2e-16
#> 


### Groups ----

# Simple regression - weights within df
replm(formula = Math1 ~ 1 + GENDER,
      wt = "wt", # Name of total weight column within df
      repwt = "REPWT", # Common names of replicate weights within df
      df = cbind(repdata2,RW), # Data frame
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> 50 weights found.
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 204 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.4976     0.0339  14.695
#> GENDER       -0.9731     0.0476 -20.462
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER, df = cbind(repdata2, RW), 
#>     wt = "wt", repwt = "REPWT", group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)   GENDER       
#> GR1 -0.076 (0.06) -0.976 (0.08)
#> GR3  1.048 (0.06) -1.002 (0.08)
#> GR2  0.520 (0.06) -0.941 (0.09)

# Simple regression - weights as a separate data frame
replm(formula = Math1 ~ 1 + GENDER,
      wt = "wt", # Name of total weight column within df
      repwt = RW, # Data frame of weights
      df = repdata2, # Data frame
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 204 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.4976     0.0339  14.695
#> GENDER       -0.9731     0.0476 -20.462
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER, df = repdata2, wt = "wt", 
#>     repwt = RW, group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)   GENDER       
#> GR1 -0.076 (0.06) -0.976 (0.08)
#> GR3  1.048 (0.06) -1.002 (0.08)
#> GR2  0.520 (0.06) -0.941 (0.09)

# Multiple regression
replm(formula = Math1 ~ 1 + GENDER + Reading1,
      wt = "wt", # Name of total weight column within df
      repwt = RW, # Data frame of weights
      df = repdata2, # Data frame
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 204 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.5047     0.0379  13.322
#> GENDER       -0.9593     0.0483 -19.854
#> Reading1     -0.0201     0.0311  -0.646
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math1 ~ 1 + GENDER + Reading1, df = repdata2, 
#>     wt = "wt", repwt = RW, group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)   GENDER        Reading1     
#> GR1 -0.010 (0.08) -1.013 (0.08)  0.066 (0.05)
#> GR3  1.048 (0.06) -1.002 (0.08)  0.000 (0.06)
#> GR2  0.475 (0.06) -0.863 (0.09) -0.127 (0.05)

# Multiple regression - with PVs
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading1, # Math1 now is "Math"
      wt = "wt", # Name of total weight column within df
      repwt = RW, # Data frame of weights
      df = repdata2, # Data frame
      pvs = pvs, # Named list
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 612 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.5157     0.0473  10.899
#> GENDER       -0.9789     0.0611 -16.018
#> Reading1      0.0594     0.0592   1.003
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading1, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)  GENDER        Reading1     
#> GR1 0.027 (0.10) -0.974 (0.09)  0.126 (0.09)
#> GR3 1.019 (0.07) -1.022 (0.10)  0.058 (0.08)
#> GR2 0.501 (0.07) -0.941 (0.12) -0.005 (0.13)

# Multiple regression - with more than one related PV variable
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3),
           Reading = paste0("Reading",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 
#> $Reading
#> [1] "Reading1" "Reading2" "Reading3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading, # Reading1 now is "Reading"
      wt = "wt", # Name of total weight column within df
      repwt = RW, # Data frame of weights
      df = repdata2, # Data frame
      pvs = pvs, # Named list
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 612 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.5584     0.0875   6.382
#> GENDER       -1.0350     0.0818 -12.654
#> Reading1      0.1110     0.1030   1.078
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, df = repdata2, 
#>     wt = "wt", repwt = RW, group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)  GENDER        Reading1    
#> GR1 0.131 (0.23) -1.061 (0.11) 0.206 (0.19)
#> GR3 1.018 (0.08) -1.061 (0.11) 0.089 (0.13)
#> GR2 0.526 (0.10) -0.983 (0.19) 0.038 (0.21)

# Multiple regression - with UNrelated PV variables
## Named list, with element names matching formula variables
pvs = list(Math = paste0("Math",1:3),
           Reading = paste0("Reading",1:3))
pvs
#> $Math
#> [1] "Math1" "Math2" "Math3"
#> 
#> $Reading
#> [1] "Reading1" "Reading2" "Reading3"
#> 

replm(formula = Math ~ 1 + GENDER + Reading, # Reading1 now is "Reading"
      wt = "wt", # Name of total weight column within df
      repwt = RW, # Data frame of weights
      df = repdata2, # Data frame
      pvs = pvs, # Named list
      relatedpvs = FALSE, # Unrelated PVs
      group = "GROUP",
      method = "ICILS") # the name of the method aka the study name
#> Estimating pooled model.
#> Estimating group 1 of 3.
#> Estimating group 2 of 3.
#> Estimating group 3 of 3.
#> 1836 models were estimated.
#> -------------------------------------------------------------------------------- 
#> Composite coefficients:
#>             Estimate Std. Error t value
#> (Intercept)   0.5648     0.0654   8.638
#> GENDER       -1.0512     0.0715 -14.703
#> Reading1      0.1368     0.0669   2.044
#> -------------------------------------------------------------------------------- 
#> 
#> Call:
#> replm(formula = Math ~ 1 + GENDER + Reading, pvs = pvs, relatedpvs = FALSE, 
#>     df = repdata2, wt = "wt", repwt = RW, group = "GROUP", method = "ICILS")
#> 
#> Coefficients and standard errors by group:
#>     (Intercept)  GENDER        Reading1    
#> GR1 0.146 (0.17) -1.070 (0.13) 0.221 (0.12)
#> GR3 1.011 (0.07) -1.079 (0.10) 0.118 (0.09)
#> GR2 0.537 (0.08) -1.004 (0.14) 0.071 (0.13)