statsModelSeries {pedometrics}

Obtain performance statistics of a series of linear models

Description

Compute several statistics measuring the performance of a series of linear models built using buildModelSeries(), with an option to rank the models based on one of the returned performance statistics.

Usage

statsModelSeries(model, design.info, arrange.by, digits)

statsMS(model, design.info, arrange.by, digits)

Arguments

model

A list of linear models returned by buildModelSeries().

design.info

Extra information about the linear models in the series.

arrange.by

Character string defining if the table with the performance statistics of the linear models should be arranged, and which column should be used. Available options are "candidates", "df", "aic", "rmse", "nrmse", "r2", "adj_r2", and "ADJ_r2". Descending order is used by default and cannot be changed in the current implementation. See ‘Value’ for more information.

digits

Integer or vector with six integers indicating the number of decimal places to be used to round the performance statistics. If a vector is passed to the function, the number of decimal places should be in the following order:

c("aic", "rmse", "nrmse", "r2", "adj_r2", "ADJ_r2").

Details

This function was devised to deal with a list of linear models generated by the function buildModelSeries(). The main objective is to compare several linear models using several performance statistics. Such statistics can then be used to rank the linear models and identify, for example, the best performing model, given the selected performance statistics.

An important feature of buildModelSeries() is that it uses the information about the initial number of candidate predictor variables offered to the build the model to calculate penalized or adjusted measures of model performance. Such information is recorded as an attribute of the final model selected by buildModelSeries(). This feature was included in statsModelSeries() because data-driven variable selection results biased linear models (too optimistic), and the effective number of degrees of freedom is close to the number of candidate predictor variables initially offered to the model (Harrell, 2001).

Value

A data frame with several performance statistics:

id

Identification of the model.

candidates

Number of candidate predictor variables initially offered to the model.

df

Number of degrees of freedom of the final selected model.

aic

Akaike's Information Criterion (AIC). Obtained using extractAIC.

rmse

Root-mean squared error, calculated based on the number of candidate predictor variables initially offered to the model.

nrmse

Normalized Root-mean squared error, calculated as the ratio between the RMSE and the standard deviation of the observed values of the dependent variable.

r2

Multiple coefficient of determination.

adj_r2

Adjusted multiple coefficient of determination.

ADJ_r2

Adjusted multiple coefficient of determination. Calculations are done based on the number of candidate predictor variables initially offered to the model.

TODO

• Include other performance statistics such as: PRESS, BIC, Mallow's Cp, max(VIF);

• Add option to select which performance statistics should be returned.

Author(s)

Alessandro Samuel-Rosa [e-mail]

References

Harrell, F. E. (2001) Regression modelling strategies: with applications to linear models, logistic regression, and survival analysis. First edition. New York: Springer.

Venables, W. N. and Ripley, B. D. (2002) Modern applied statistics with S. Fourth edition. New York: Springer.

A. Samuel-Rosa, G. B. M. Heuvelink, G. de Mattos Vasques, and L. H. C. dos Anjos, Do more detailed environmental covariates deliver more accurate soil maps?, Geoderma, vol. 243–244, pp. 214–227, May 2015, doi: 10.1016/j.geoderma.2014.12.017.

See Also

buildModelSeries(), plotModelSeries()

Examples

if (interactive()) {
  # based on the second example of function MASS:stepAIC()
  require(MASS)
  cpus1 <- cpus
  for(v in names(cpus)[2:7])
    cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])), 
                      include.lowest = TRUE)
  cpus0 <- cpus1[, 2:8]  # excludes names, authors' predictions
  cpus.samp <- sample(1:209, 100)
  cpus.form <- list(formula(log10(perf) ~ syct + mmin + mmax + cach + chmin +
                    chmax + perf),
                    formula(log10(perf) ~ syct + mmin + cach + chmin + chmax),
                    formula(log10(perf) ~ mmax + cach + chmin + chmax + perf))
  data <- cpus1[cpus.samp,2:8]
  cpus.ms <- buildModelSeries(cpus.form, data, vif = TRUE, aic = TRUE)
  cpus.des <- data.frame(a = c(0, 1, 0), b = c(1, 0, 1), c = c(1, 1, 0))
  stats <- statsModelSeries(cpus.ms, design.info = cpus.des, arrange.by = "aic")
}