A Appendix A: R as a Statistical Programming Language

A.1 Overview

library(knitr)
  • Why use Statistical Programming Languages?

Computers and Programs

  • Fixed program computer
    • programs are “hard-wired” into computer
    • calculator, stopwatch
  • Stored program computer
    • machine stores and executes instructions
    • most modern computers, your phone, etc.

Statistical Programs versus Statistical Programming Language

  • Statistical Programs
    • fixed menus
    • limited procedures (at least in the menus)
    • leads to compartmentalizing models (e.g. ANOVA, regression, GLM)
  • Statistical Programming Languages (SPLs)
    • Turing complete: if you can create an algorithm you can program it
    • Very flexible
    • Integration of models: One model to rule them all!

Everythin

A.2 Elements of Statistical Programming

A.2.1 Basic Elements of a Good SPL

  1. a rich set of primitive expressions
  2. mechanisms for combining expressions into more complex expressions
  3. means of abstraction, which allow for naming and manipulating compound objects

A.3 Expressions

A.4 Primitive Expressions

  • Everything in R is an object

  • Primitive objects are the simplest elements of a programming language, and include:

    • primitive data
    • primitive functions

  • They can be thought of as the basic building blocks for everything else in the language.

  • An expression is an input that the programming language can evaluate, and consists of function and data objects.

A.5 Primitive Data Types:

Data objects are the primary means of storing information in R. R has a few basic data types:

  • Numeric -

    • numeric
      • int - integers (1,2)
      • num - real number (1.2, -3.1, 200.0)

  • character or string -

    • character
      • "Hello world!", "Ten", 'Cat'
      • "This is a sentence, which is a string"
      • "10" ( in single or double quotes, as long as they match)

  • Boolean or Logical

    • logical
      • TRUE or FALSE (use operators such as or, and and not).
      • They will evaluate to numbers where FALSE evaluates to zero, and TRUE evaluates to one.
      • For example. if you enter TRUE + 1 you will get 2 in return.
mode(TRUE)
## [1] "logical"
TRUE + 1
## [1] 2

A.6 Primitive Functions

R uses functions to do all computations.

A.6.1 Operators

  • Arithmetic Operators
    • +, -, *, /, ^
  • Comparison (also called Boolean, Logical or Predicate) Operators
    • <, >, ==, <=, >=, !=
    • less than, greater than, equal to, less than or equal to, greater than or equal to, not equal to
    • return TRUE or FALSE
  • Logical Operator
    • &, | ,!
    • also return TRUE or FALSE
  • Other functions
    • mode()
    • length()
    • sum()
    • sqrt()
    • log()
    • exp()
  • Assignment operators (assignment will be discussed below)
    • <- preferred assignment operator - always use this one
    • = this will also work, but can be confusing (note different from ==, the comparison operator)
    • -> is also an assignment operator, but we will not use it.

A.7 Programming Languages are Not Forgiving

A.7.1 Syntactically valid expressions

Expressions must be syntactically valid.

  • syntax (form)
    • English: “cat dog boy” - not syntactically valid
    • English: “cat hugs boy” - syntactically valid
  • programming language:
    • “hi” 5 - not syntactically valid
    • 3.2*5 - syntactically valid

A.7.2 Semantically valid expressions

  • semantics - (meaning)
    • English: “I are hungry” - syntactically valid but semantic error
    • programming language:
      • 3 + “hi” - semantic error (you can’t use addition on character strings)
  • Chomsky: “colorless green ideas sleep furiously”

This statement is syntactically valid, but does not make sense, so makes a semantic error.

A.8 Assignment

We will often want to save data in a variable. We can do that with assignment, which utilizes an assignment operator.

x <- 2
x
## [1] 2
pet <- "dog"
pet
## [1] "dog"

A.9 Combining Expressions

A.10 Complex Data Types

  • Scalars, Vectors, Matrices, and Arrays
  • Lists
  • Dataframes

A.11 Grouping Homogeneous Data Types

  • combining scalars
c()
  • combining expressions
{}
  • combining vectors
cbind()
rbind()

A.12 Complex Functions

  • Vectorization
  • Nested Functions
  • Loops and Conditional execution

class: inverse, center, middle

A.13 Abstraction

A.14 Abstraction

  • Assignment

A.15 Data Abstraction

A.16 Functional Abstraction

A.17 Anatomy of a Function

name <- function(arg_1, arg_2, ...) expression

A.18 Teaching With A Statistical Programming Language

A.18.1 An Example

A.19 myMean

A.20 Basic Elements of a Good SPL

A rich set of primitive expressions

Mechanisms for combining expressions into more complex expressions

Means of abstraction, which allow for naming and manipulating compound objects

Judd, Charles M, Gary H McClelland, and Carey S Ryan. 2017. Data Analysis: A Model Comparison Approach to Regression, ANOVA, and Beyond. Routledge.