Hierarchical Regression Analysis

Do hierarchical regression analysis on two or more models fitted by 'lm()'.

Usage

hierarchical_lm(...)

Arguments

...: The outputs of lm(), that is, one or more lm-class objects. The outputs of other model fitting functions may also be used, but should be used with cautions. Please refer to the "How it works" section in "Details."

Value

If the models can be ordered in a hierarchical way, the output is an ANOVA table with the R-squared estimate of each model, and the R-squared change of each model compared to the simpler model preceding this model in the order. The class of the output is hierarchical_lm, with a print method. If the models cannot be ordered this way, NA is returned.

How it works

It call hierarchical() firsts to order the outputs for stats::lm(), If they can be ordered in a hierarchical way, they will be passed to stats::anova(). R-squared and R-squared change will be computed if they are available in the summary() method applied to each model.

Therefore, in principle, this function can also be used for the outputs of other model fitting functions if their outputs have stats::anova() and summary() methods.

Check Datasets Used

The comparison is meaningful only if all models are fitted to the same datasets. There is not way to guarantee this is the case, given only the output of lm(). However, there are necessary conditions to claim that the same datasets are used: the number of cases are the same, the means, variances, and covariances of numerical variables, and the frequency distributions of variables common to two models are identical. If at least one of these conditions is not met, then two models must have been fitted to two different datasets.

The function will check these conditions and raise an error if any of these necessary conditions are not met.

Details

It conducted hierarchical regression analysis on two or more models fitted by stats::lm(). The models must be able to be ordered from the simplest to the most complex, with each more complex model formed by adding one or more terms to the simpler model.

ANOVA will be conducted to compare each model with the next more complex model in the order, with R-squared change computed.

Author

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

Examples


dat <- data_test1
lm1 <- lm(y ~ x1 + x2, dat)
lm2 <- lm(y ~ x1 + x2 + x3 + x4, dat)
lm3 <- lm(y ~ x1 + cat1 + cat2 + x2 + x3 + x4, dat)
lm4 <- lm(y ~ x1 + x2*x3 + x4, dat)

hierarchical_lm(lm1, lm3, lm2)
#> Analysis of Variance Table
#> 
#> Model 1: y ~ x1 + x2
#> Model 2: y ~ x1 + x2 + x3 + x4
#> Model 3: y ~ x1 + cat1 + cat2 + x2 + x3 + x4
#>   adj.R.sq   R.sq R.sq.change Res.Df   RSS Df Sum of Sq      F Pr(>F)    
#> 1   0.5090 0.5189     0.00000     97 55.83                               
#> 2   0.7269 0.7380     0.21906     95 30.41  2    25.419 39.717 <0.001 ***
#> 3   0.7270 0.7518     0.01385     90 28.80  5     1.607  1.004   0.42    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
hierarchical_lm(lm1, lm2, lm4)
#> Analysis of Variance Table
#> 
#> Model 1: y ~ x1 + x2
#> Model 2: y ~ x1 + x2 + x3 + x4
#> Model 3: y ~ x1 + x2 * x3 + x4
#>   adj.R.sq   R.sq R.sq.change Res.Df   RSS Df Sum of Sq      F Pr(>F)    
#> 1   0.5090 0.5189      0.0000     97 55.83                               
#> 2   0.7269 0.7380      0.2191     95 30.41  2    25.419 39.320 <0.001 ***
#> 3   0.7242 0.7382      0.0002     94 30.38  1     0.024  0.073  0.787    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# The following models will yield an error message:
tryCatch(hierarchical_lm(lm1, lm3, lm2, lm4), error = function(e) e)
#> <simpleError in hierarchical_lm(lm1, lm3, lm2, lm4): The models do not have hierarchical relations.>