Think Stats: Getting Started

December 11, 2015
clojure incanter statistics

One of our new starters here at Metail was keen to brush up his statistics, and it’s more than 20 years since I completed an introductory course at university so I knew I would benefit from some revision. We also have a bunch of statisticians in the office who would like to brush up their Clojure, so I thought it might be fun to organise a lunchtime study group to work through Allen Downey’s Think Stats and attempt the exercises in Clojure.

We’ll use Clojure’s Incanter library which provides utilities for statistical analysis and generating charts. Create a Leiningen project for our work:

lein new thinkstats

Make sure the project.clj depends on Clojure 1.7.0 and add a dependency on Incanter 1.5.6:

:dependencies [[org.clojure/clojure "1.7.0"]
               [incanter "1.5.6"]]

We’re using the second edition of the book which is available online in HTML format, and meeting on Wednesday lunchtimes to work through it together.

Parsing the data

In the first chapter of the book, we are introduced to a data set from the US Centers for Disease Control and Prevention, the National Survey of Family Growth. The data are in a gzipped file with fixed-with columns. An accopanying Stata dictionary describes the variable names, types, and column idicces for each record. Our first job will be to parse the dictionary file and use that information to build a parser for the data.

I cloned the Github repository that accompanies Allen’s book:

git clone https://github.com/AllenDowney/ThinkStats2

Then created symlinks to the data files from my project:

cd thinkstats
mkdir data
cd data
for f in ../../ThinkStats2/{*.dat.gz,*.dct}; do ln -s $f; done

I can now read the Stata dictionary for the familiy growth study from data/2002FemPreg.dct. The dictionary looks like:

infile dictionary {
    _column(1)  str12    caseid     %12s  "RESPONDENT ID NUMBER"
    _column(13) byte     pregordr   %2f  "PREGNANCY ORDER (NUMBER)"
}

If we skip the first and last lines of the dictionary, we can use a regular expression to parse each column defitinion:

(def dict-line-rx #"^\s+_column\((\d+)\)\s+(\S+)\s+(\S+)\s+%(\d+)(\S)\s+\"([^\"]+)\"")

We’re capturing the column position, colum type, column name, format and length, and description. Let’s test this at the REPL. First we have to read a line from the dictionary:

(require '[clojure.java.io :as io])
(def line (with-open [r (io/reader "data/2002FemPreg.dct")]
            (first (rest (line-seq r)))))

We use rest to skip the first line of the file then grab the first column definition. Now we can try matching this with our regular expression:

(re-find dict-line-rx line)

This returns the string that matched and the capture groups we defined in our regular expression:

["    _column(1)      str12                             caseid  %12s  \"RESPONDENT ID NUMBER\""
 "1"
 "str12"
 "caseid"
 "12"
 "s"
 "RESPONDENT ID NUMBER"]

We need to do some post-processing of this result to parse the column index and length to integers; we’ll also replace underscores in the column name with hyphens, which makes for a more idiomatic Clojure variable name. Let’s wrap that up in a function:

(require '[clojure.string :as str])

(defn parse-dict-line
  [line]
  (let [[_ col type name f-len f-spec descr] (re-find dict-line-rx line)]
    {:col    (dec (Integer/parseInt col))
     :type   type
     :name   (str/replace name "_" "-")
     :f-len  (Integer/parseInt f-len)
     :f-spec f-spec
     :descr  descr}))

Note that we’re also decrementing the column index - we need zero-indexed column indices for Clojure’s substring function. Now when we parse our sample line we get:

{:col 0,
 :type "str12",
 :name "caseid",
 :f-len 12,
 :f-spec "s",
 :descr "RESPONDENT ID NUMBER"}

With this function in hand, we can write a parser for the dictionary file:

(defn read-dict-defn
  "Read a Stata dictionary file, return a vector of column definitions."
  [path]
  (with-open [r (io/reader path)]
    (mapv parse-dict-line (butlast (rest (line-seq r))))))

We use rest and butlast to skip the first and last lines of the file, and mapv to force eager evaluation and ensure we process all of the input before the reader is closed when we exit with-open.

(def dict (parse-dict-defn "data/2002FemPreg.dat"))

We’re going to use subs to extract the raw value of each column from the data. This will give us a string, and the :type key we’ve extracted from the dictionary tells us how to interpret this. We’ve seen the types str12 and byte above, but what other types appear in the dictionary?

(distinct (map :type dict))
;=> ("str12" "byte" "int" "float" "double")

We’ll leave str12 unchanged, coerce byte and int to Long, and float and double to Double:

(defn parse-value
  [type raw-value]
  (when (not (empty? raw-value))
    (case type
      ("str12")          raw-value
      ("byte" "int")     (Long/parseLong raw-value)
      ("float" "double") (Double/parseDouble raw-value))))

We can now build a record parser from the dictionary definition:

(defn make-row-parser
  "Parse a row from a Stata data file according to the specification in `dict`.
   Return a vector of columns."
  [dict]
  (fn [row]
    (reduce (fn [accum {:keys [col type name f-len]}]
              (let [raw-value (str/trim (subs row col (+ col f-len)))]
                (conj accum (parse-value type raw-value))))
            []
            dict)))

To read gzipped data, we need to open an input stream, coerce this to a GZIPInputStream, and construct a buffered reader from that. For convenience, we’ll define a function to do this automatically if passed a path ending in .gz.

(import 'java.util.zip.GZIPInputStream)

(defn reader
  "Open path with io/reader; coerce to a GZIPInputStream if suffix is .gz"
  [path]
  (if (.endsWith path ".gz")
    (io/reader (GZIPInputStream. (io/input-stream path)))
    (io/reader path)))

Give a dictionary and reader, we can parse the records from a data file:

(defn read-dct-data
  "Parse lines from `rdr` according to the specification in `dict`.
   Return a lazy sequence of parsed rows."
  [dict rdr]
  (let [parse-fn (make-row-parser dict)]
    (map parse-fn (line-seq rdr))))

Finally, we bring this all together with a function to parse the dictionary and data and return an Incanter dataset:

(require '[incanter.core :refer [dataset]])

(defn as-dataset
  "Read Stata data set, return an Incanter dataset."
  [dict-path data-path]
  (let [dict   (read-dict-defn dict-path)
        header (map (comp keyword :name) dict)]
    (with-open [r (reader data-path)]
      (dataset header (doall (read-dct-data dict r))))))

Getting the code

The code for all this is available on Github; if you’d like to follow along, you can fork my thinkstats repository.

The functions for parsing Stata dictionary files are in the namespace thinkstats.dct-parser. In the next article in this series, we use the parser to explore and clean the dataset with Incanter.

This article originally appeared in the Metail Tech Blog.

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