linear2btl: Linear Coefficients to Bradley-Terry-Luce (BTL) Estimates

In eba: Elimination-by-Aspects Models

Description

Transforms linear model coefficients to Bradley-Terry-Luce (BTL) model parameter estimates.

Usage

linear2btl(object, order = FALSE)

Arguments

object	an object of class glm or lm specifying a BTL model
order	logical, does the model include an order effect? Defaults to FALSE

Details

The design matrix used by glm or lm usually results from a call to pcX. It is assumed that the reference category is the first level. The covariance matrix is estimated by employing the delta method. See Imrey, Johnson, and Koch (1976) for more details.

Value

btl.parameters	a matrix; the first column holds the BTL parameter estimates, the second column the approximate standard errors
cova	the approximate covariance matrix of the BTL parameter estimates
linear.coefs	a vector of the original linear coefficients as returned by glm or lm

References

Imrey, P.B., Johnson, W.D., & Koch, G.G. (1976). An incomplete contingency table approach to paired-comparison experiments. Journal of the American Statistical Association, 71, 614–623. doi: 10.2307/2285591

See Also

eba, eba.order, glm, pcX.

Examples

data(drugrisk)
y1 <- t(drugrisk[, , 1])[lower.tri(drugrisk[, , 1])]
y0 <-   drugrisk[, , 1][ lower.tri(drugrisk[, , 1])]

## Fit BTL model using glm (maximum likelihood)
btl.glm <- glm(cbind(y1, y0) ~ 0 + pcX(6), binomial)
linear2btl(btl.glm)

## Fit BTL model using lm (weighted least squares)
btl.lm <- lm(log(y1/y0) ~ 0 + pcX(6), weights=y1*y0/(y1 + y0))
linear2btl(btl.lm)

Example output

$btl.parameters
           estimate          se
        0.019008209 0.004754588
pcX(6)1 0.014786508 0.003805432
pcX(6)2 0.009350402 0.002539089
pcX(6)3 0.167877536 0.029825405
pcX(6)4 0.604458817 0.053500761
pcX(6)5 0.184518527 0.032155050

$cova
              h                                                        
h  2.260610e-05  1.163555e-05  7.658454e-06  4.320552e-05 -1.278855e-04
   1.163555e-05  1.448131e-05  6.253761e-06  3.372737e-05 -9.947951e-05
   7.658454e-06  6.253761e-06  6.446971e-06  2.138760e-05 -6.290748e-05
   4.320552e-05  3.372737e-05  2.138760e-05  8.895548e-04 -1.214332e-03
  -1.278855e-04 -9.947951e-05 -6.290748e-05 -1.214332e-03  2.862331e-03
   4.277986e-05  3.338151e-05  2.116070e-05  2.264572e-04 -1.357726e-03
               
h  4.277986e-05
   3.338151e-05
   2.116070e-05
   2.264572e-04
  -1.357726e-03
   1.033947e-03

$linear.coefs
   pcX(6)1    pcX(6)2    pcX(6)3    pcX(6)4    pcX(6)5 
-0.2511558 -0.7094516  2.1783638  3.4594626  2.2728789 

$btl.parameters
          estimate          se
        0.02268394 0.005231406
pcX(6)1 0.01818484 0.004549953
pcX(6)2 0.01244278 0.003256660
pcX(6)3 0.16018025 0.029897451
pcX(6)4 0.59402701 0.053218843
pcX(6)5 0.19248117 0.033218284

$cova
              h                                                        
h  2.736761e-05  1.441924e-05  1.010296e-05  3.154721e-05 -1.187031e-04
   1.441924e-05  2.070207e-05  9.140673e-06  2.082393e-05 -9.412027e-05
   1.010296e-05  9.140673e-06  1.060583e-05  1.168456e-05 -6.197128e-05
   3.154721e-05  2.082393e-05  1.168456e-05  8.938576e-04 -1.163586e-03
  -1.187031e-04 -9.412027e-05 -6.197128e-05 -1.163586e-03  2.832245e-03
   3.526607e-05  2.903435e-05  2.043726e-05  2.056726e-04 -1.393865e-03
               
h  3.526607e-05
   2.903435e-05
   2.043726e-05
   2.056726e-04
  -1.393865e-03
   1.103454e-03

$linear.coefs
   pcX(6)1    pcX(6)2    pcX(6)3    pcX(6)4    pcX(6)5 
-0.2210691 -0.6005164  1.9546424  3.2652675  2.1383410 

eba documentation built on Jan. 13, 2021, 10:12 a.m.