A higher-order function is a function that takes one or more functions as arguments, and\or returns a function as its result. This can be super handy in programming when you want to tilt your code towards readability and still keep it concise.

Consider the following code:

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# Generate some fake data > eps <- rnorm(10, sd= 5) > x <- c(1:10) > y <- 2+2*x + eps # Load libraries required > library(quantreg) > library(magrittr) > eps <- rnorm(10, sd= 5) > x <- c(1:10) > y <- 2+2*x + eps # create a higher order function > higher_order_function <- function(func){ + func(y ~ x) %>% summary + } > # Give as an argument the function "lm" > higher_order_function(lm) Call: func(formula = y ~ x) Residuals: Min 1Q Median 3Q Max -12.0149 -0.7603 1.0969 2.7483 4.2373 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.3214 3.3338 0.396 0.70219 x 2.1690 0.5373 4.037 0.00375 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.88 on 8 degrees of freedom Multiple R-squared: 0.6708, Adjusted R-squared: 0.6296 F-statistic: 16.3 on 1 and 8 DF, p-value: 0.003751 # Now give as an argument the function rq (for regression quantile) > higher_order_function(rq) Call: func(formula = y ~ x) tau: [1] 0.5 Coefficients: coefficients lower bd upper bd (Intercept) 3.80788 -1.26475 6.15759 x 1.83968 1.59747 2.98423 |

It’s also quite safe to use in that if you provide a non-existent function it would not default to some unknown behavior but will return an error:

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> higher_order_function(mm) Error in eval(lhs, parent, parent) : object 'mm' not found |

However, this function can be also written as a sequence of if statements, like so

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> if_function <- function(x,y, which_reg){ + if (which_reg== "OLS") { lm(y~x) %>% summary } + else if (which_reg== "LAD") { rq(y~x) %>% summary } + } > if_function(x,y, which_reg= "OLS") Call: lm(formula = y ~ x) Residuals: Min 1Q Median 3Q Max -12.0149 -0.7603 1.0969 2.7483 4.2373 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.3214 3.3338 0.396 0.70219 x 2.1690 0.5373 4.037 0.00375 ** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.88 on 8 degrees of freedom Multiple R-squared: 0.6708, Adjusted R-squared: 0.6296 F-statistic: 16.3 on 1 and 8 DF, p-value: 0.003751 > if_function(x,y, which_reg= "LAD") Call: rq(formula = y ~ x) tau: [1] 0.5 Coefficients: coefficients lower bd upper bd (Intercept) 3.80788 -1.26475 6.15759 x 1.83968 1.59747 2.98423 |

Using higher-order functions does not seem to create any additional computational cost:

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> library(microbenchmark) > microbenchmark( higher_order_function(rq), if_function(x, y, "LAD") ) Unit: milliseconds expr min lq mean median uq higher_order_function(rq) 1.463210 1.498967 1.563553 1.527253 1.624969 if_function(x, y, "LAD") 1.468262 1.498464 1.584453 1.618997 1.644462 max neval 2.280419 100 2.082765 100 > microbenchmark( higher_order_function(lm), if_function(x, y, "OLS") ) Unit: microseconds expr min lq mean median uq max higher_order_function(lm) 916.858 928.8825 946.9838 935.3930 955.791 1025.575 if_function(x, y, "OLS") 918.674 928.1260 953.2587 938.0465 958.284 1433.167 neval 100 100 |

So you can make your code more concise with little computational overhead.

Thank you, very interesting application of higher-order functions.

This post that I wrote some time ago might be a good starting point to understand how to use higher-order functions: http://blog.ephorie.de/learning-r-a-gentle-introduction-to-higher-order-functions