maxLik (version 0.6-0)

condiNumber: Print matrix condition numbers column-by-column

Description

This function prints the condition number of a matrix while adding columns one-by-one. This is useful for testing multicollinearity and other numerical problems. This is a generic function with default method and method for maxLik objects.

Usage

condiNumber(x, ...)
## S3 method for class 'default':
condiNumber(x, exact = FALSE, norm = FALSE,
print.level=1, ...)
## S3 method for class 'maxLik':
condiNumber(x, ...)

Arguments

x

numeric matrix, condition numbers of which are to be printed

exact

logical, should condition numbers be exact or approximations (see link{kappa})

norm

logical, whether the columns should be normalised to have unit norm

print.level

numeric, positive value will output the numbers during the calculations. Useful for interactive work.

...

other arguments to different methods

Value

• Invisible vector of condition numbers by column.

Details

Statistical model often fail because of strong correlation between explanatory variables in linear index (multicollinearity) or because the evaluated maximum of a non-linear model is virtually flat. In both cases, the (near) singularity of the related matrices may give us a hint, how to improve the results.

condiNumber allows to inspect the matrices column-by-column and unerstand which variable leads to a huge jump in the condition number. If the single column does not immediately tell what is the problem, one may try to estimate this column by OLS using the previous columns as explanatory variables. The columns, which explain virtually all the variation, should have extremely high t-values.

References

W. Greene, Advanced Econometrics, p ...

See Also

kappa

Examples

set.seed(0)
   ## generate a simple multicollinear dataset
   x1 <- runif(100)
   x2 <- runif(100)
   x3 <- x1 + x2 + 0.000001*runif(100) # this is virtually equal to x1 + x2
   x4 <- runif(100)
   y <- x1 + x2 + x3 + x4 + rnorm(100)
   m <- lm(y ~ -1 + x1 + x2 + x3 + x4)
   print(summary(m)) # note the low t-values while R^2 is 0.88.
                     # This hints multicollinearity
   condiNumber(model.matrix(m)) # this _prints_ condition numbers.
                                # note the values 'explode' with x3
   ## we may test the results further:
   print(summary(lm(x3 ~ -1 + x1 + x2))) # Note the high t-values and R^2