This blog is a companion to my recent book, Exploring Data in Engineering, the Sciences, and Medicine, published by Oxford University Press. The blog expands on topics discussed in the book, and the content is heavily example-based, making extensive use of the open-source statistical software package R.

Saturday, October 27, 2012

Characterizing a new dataset

In my last post, I promised a further examination of the spacing measures I described there, and I still promise to do that, but I am changing the order of topics slightly.  So, instead of spacing measures, today’s post is about the DataframeSummary procedure to be included in the ExploringData package, which I also mentioned in my last post and promised to describe later.  My next post will be a special one on Big Data and Data Science, followed by another one about the DataframeSummary procedure (additional features of the procedure and the code used to implement it), after which I will come back to the spacing measures I discussed last time.

A task that arises frequently in exploratory data analysis is the initial characterization of a new dataset.  Ideally, everything we could want to know about a dataset should come from the accompanying metadata, but this is rarely the case.  As I discuss in Chapter 2 of Exploring Data in Engineering, the Sciences, and Medicine, metadata is the available “data about data” that (usually) accompanies a data source.  In practice, however, the available metadata is almost never as complete as we would like, and it is sometimes wrong in important respects.  This is particularly the case when numeric codes are used for missing data, without accompanying notes describing the coding.  An example, illustrating the consequent problem of disguised missing data is described in my paper The Problem of Disguised Missing Data.  (It should be noted that the original source of one of the problems described there – a comment in the UCI Machine Learning Repository header file for the Pima Indians diabetes dataset that there were no missing data records – has since been corrected.)

Once we have converted our data source into an R data frame (e.g., via the read.csv function for an external csv file), there are a number of useful tools to help us begin this characterization process.  Probably the most general is the str command, applicable to essentially any R object.  Applied to a dataframe, this command first tells us that the object is a dataframe, second, gives us the dimensions of the dataframe, and third, presents a brief summary of its contents, including the variable names, their type (specifically, the results of R’s class function), and the values of their first few observations.  As a specific example, if we apply this command to the rent dataset from the gamlss package, we obtain the following summary:

> str(rent)
'data.frame':   1969 obs. of  9 variables:
 $ R  : num  693 422 737 732 1295 ...
 $ Fl : num  50 54 70 50 55 59 46 94 93 65 ...
 $ A  : num  1972 1972 1972 1972 1893 ...
 $ Sp : num  0 0 0 0 0 0 0 0 0 0 ...
 $ Sm : num  0 0 0 0 0 0 0 0 0 0 ...
 $ B  : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
 $ H  : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 1 1 1 ...
 $ L  : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
 $ loc: Factor w/ 3 levels "1","2","3": 2 2 2 2 2 2 2 2 2 2 ...
> 
This dataset summarizes a 1993 random sample of housing rental prices in Munich, including a number of important characteristics about each one (e.g., year of construction, floor space in square meters, etc.).  A more detailed description can be obtained via the command “help(rent)”.

The head command provides similar information to the str command, in slightly less detail (e.g., it doesn’t give us the variable types), but in a format that some will find more natural:

> head(rent)
       R Fl    A Sp Sm B H L loc
1  693.3 50 1972  0  0 0 0 0   2
2  422.0 54 1972  0  0 0 0 0   2
3  736.6 70 1972  0  0 0 0 0   2
4  732.2 50 1972  0  0 0 0 0   2
5 1295.1 55 1893  0  0 0 0 0   2
6 1195.9 59 1893  0  0 0 0 0   2
> 
 (An important difference between these representations is that str characterizes factor variables by their level number and not their level value: thus the first few observations of the factor B assume the first level of the factor, which is the value 0.  As a consequence, while it may appear that str is telling us that the first few records list the value 1 for the variable B while head is indicating a zero, this is not the case.  This is one reason that data analysts may prefer the head characterization.)

While the R data types for each variable can be useful to know – particularly in cases where it isn’t what we expect it to be, as when integers are coded as factors – this characterization doesn’t really tell us the whole story.  In particular, note that R has commands like “as.character” and “as.factor” that can easily convert numeric variables to character or factor data types.  Even beyond this, the range of inherent behaviors that numerically-coded data can exhibit cannot be fully described by a simple data type designation.  As a specific example, one of the variables in the rent dataframe is “A,” described in the metadata available from the help command as “year of construction.”  While this variable is coded as type “numeric,” in fact it takes integer values from 1890 to 1988, with some values in this range repeated many times and others absent.  This point is important, since analysis tools designed for continuous variables – especially outlier-resistant ones like medians and other rank-based methods – sometimes perform poorly in the face of data sequences with many repeated values (i.e., “ties,” which have zero probability for continuous data distributions).  In extreme cases, these techniques may fail completely, as in the case of the MADM scale estimate, discussed in Chapter 7 of Exploring Data.  This data characterization implodes if more than 50% of the data values are the same, returning the useless value zero in this case, independent of the values of all of the other data points.

These observations motivate the DataframeSummary procedure described here, to be included in the ExploringData package.  This function is called with the name of the dataframe to be characterized and an optional parameter Option, which can take any one of the following four values:

  1. “Brief” (the default value)
  2. “NumericOnly”
  3. “FactorOnly”
  4. “AllAsFactor”

In all cases, this function returns a summary dataframe with one row for each column in the dataframe to be characterized.  Like the str command, these results include the name of each variable and its type.  Under the default option “Brief,” this function also returns the following characteristics for each variable:

  • Levels = the number of distinct values the variable exhibits;
  • AvgFreq = the average number of records listing each value;
  • TopLevel = the most frequently occurring value;
  • TopFreq = the number of records listing this most frequent value;
  • TopPct = the percentage of records listing this most frequent value;
  • MissFreq = the number of missing or blank records;
  • MissPct = the percentage of missing or blank records.

For the rent dataframe, this function (under the default “Brief” option) gives the following summary:

> DataframeSummary(rent)
Variable Type Levels AvgFreq TopLevel TopFreq TopPct MissFreq MissPct
3        A    numeric      73   26.97         1957         551       27.98         0       0
6        B    factor           2  984.50           0          1925        97.77        0       0
2       Fl     numeric      91   21.64          60              71          3.61        0       0
7        H    factor            2  984.50          0          1580        80.24        0       0
8        L    factor            2  984.50          0           1808        91.82        0       0
9      loc    factor            3  656.33          2           1247        63.33        0       0
1        R    numeric   1762    1.12          900               7          0.36        0       0
5       Sm  numeric         2  984.50           0          1797         91.26        0       0
4       Sp   numeric         2  984.50           0          1419         72.07        0       0
> 

The variable names and types appear essentially as they do in the results obtained with the str function, and the numbers to the far left indicate the column numbers from the dataframe rent for each variable, since the variable names are listed alphabetically for convenience.  The “Levels” column of this summary dataframe gives the number of unique values for each variable, and it is clear that this can vary widely even within a given data type.  For example, the variable “R” (monthly rent in DM) exhibits 1,762 unique values in 1,969 data observations, so it is almost unique, while the variables “Sm” and “Sp” exhibit only two possible values, even though all three of these variables are of type “numeric.”  The AvgFreq column gives the average number of times each level should appear, assuming a uniform distribution over all possible values.  This number is included as a reference value for assessing the other frequencies (i.e., TopFreq for the most frequently occurring value and MissFreq for missing data values).  Thus, for the first variable, “A,” AvgFreq is 26.97, meaning that if all 73 possible values for this variable were equally represented, each one should occur about 27 times in the dataset.  The most frequently occurring level (TopLevel) is “1957,” which occurs 551 times, suggesting a highly nonuniform distribution of values for this variable.  In contrast, for the variable “R,” AvgFreq is 1.12, meaning that each value of this variable is almost unique.  The TopPct column gives the percentage of records in the dataset exhibiting the most frequent value for each record, which varies from 0.36% for the numeric variable “R” to 97.77% for the factor variable “B.”  It is interesting to note that this variable is of type “factor” but is coded as 0 or 1, while the variables “Sm” and “Sp” are also binary, coded as 0 or 1, but are of type “numeric.”  This illustrates the point noted above that the R data type is not always as informative as we might like it to be.  (This is not a criticism of R, but rather a caution about the fact that, in preparing data, we are free to choose many different representations, and the original logic behind the choice may not be obvious to all ultimate users of the data.)  In addition, comparing the available metadata for the variable “B” illustrates the point about metadata errors noted earlier: of the 1,969 data records, 1,925 have the value “0” (97.77%), while 44 have the value “1” (2.23%), but the information returned by the help command indicates exactly the opposite proportion of values: 1,925 should have the value “1” (indicating the presence of a bathroom), while 44 should have the value “0” (indicating the absence of a bathroom).  Since the interpretation of the variables that enter any analysis is important in explaining our final analytical results, it is useful to detect this type of mismatch between the data and the available metadata as early as possible.  Here, comparing the average rents for records with B = 1 (DM 424.95) against those with B = 0 (DM 820.72) suggests that the levels have been reversed relative to the metadata: the relatively few housing units without bathrooms are represented by B = 1, renting for less than the majority of those units, which have bathrooms and are represented by B = 0.  Finally, the last two columns of the above summary give the number of records with missing or blank values (MissFreq) and the corresponding percentage (MissPct); here, all records are complete so these numbers are zero.

In my next post on this topic, I will present results for the other three options of the DataframeSummary procedure, along with the code that implements it.  In all cases, the results include those generated by the “Brief” option just presented, but the difference between the other options lies first, in what additional characterizations are included, and second, in which subset of variables are included in the summary.  Specifically, for the rent dataframe, we obtain:

  • Under the “NumericOnly” option, a summary of the five numeric variables R, FL, A, Sp, and Sm results, giving characteristics that are appropriate to numeric data types, like the spacing measures described in my last post;
  • Under the “FactorOnly” option, a summary of the four factor variables B, H, L, and loc results, giving measures that are appropriate to categorical data types, like the normalized Shannon entropy measure discussed in several previous posts;
  • Under the “AllAsFactor” option, all variables in the dataframe are first converted to factors and then characterized using the same measures as in the “FactorOnly” option.

The advantage of the “AllAsFactor” option is that it characterizes all variables in the dataframe, but as I discussed in my last post, the characterization of numerical variables with measures like Shannon entropy is not always terribly useful.

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