Commit 1fb57681 authored by Michiel Cottaar's avatar Michiel Cottaar Committed by Paul McCarthy
Browse files

avoiding weird error when using custom mad

parent e81c542c
...@@ -963,7 +963,7 @@ ...@@ -963,7 +963,7 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"titanic.groupby(['class', 'survived']).aggregate((np.median, mad))" "titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))"
] ]
}, },
{ {
...@@ -984,7 +984,7 @@ ...@@ -984,7 +984,7 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, mad))" "df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))"
] ]
}, },
{ {
......
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
# Pandas # Pandas
Pandas is a data analysis library focused on the cleaning and exploration of Pandas is a data analysis library focused on the cleaning and exploration of
tabular data. tabular data.
Some useful links are: Some useful links are:
- [main website](https://pandas.pydata.org) - [main website](https://pandas.pydata.org)
- [documentation](http://pandas.pydata.org/pandas-docs/stable/)<sup>1</sup> - [documentation](http://pandas.pydata.org/pandas-docs/stable/)<sup>1</sup>
- [Python Data Science Handbook](https://jakevdp.github.io/PythonDataScienceHandbook/)<sup>1</sup> by - [Python Data Science Handbook](https://jakevdp.github.io/PythonDataScienceHandbook/)<sup>1</sup> by
Jake van der Plas Jake van der Plas
- [List of Pandas tutorials](https://pandas.pydata.org/pandas-docs/stable/getting_started/tutorials.html) - [List of Pandas tutorials](https://pandas.pydata.org/pandas-docs/stable/getting_started/tutorials.html)
<sup>1</sup> This tutorial borrows heavily from the pandas documentation and <sup>1</sup> This tutorial borrows heavily from the pandas documentation and
the Python Data Science Handbook the Python Data Science Handbook
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
%pylab inline %pylab inline
import pandas as pd # pd is the usual abbreviation for pandas import pandas as pd # pd is the usual abbreviation for pandas
import matplotlib.pyplot as plt # matplotlib for plotting import matplotlib.pyplot as plt # matplotlib for plotting
import seaborn as sns # seaborn is the main plotting library for Pandas import seaborn as sns # seaborn is the main plotting library for Pandas
import statsmodels.api as sm # statsmodels fits linear models to pandas data import statsmodels.api as sm # statsmodels fits linear models to pandas data
import statsmodels.formula.api as smf import statsmodels.formula.api as smf
from IPython.display import Image from IPython.display import Image
sns.set() # use the prettier seaborn plotting settings rather than the default matplotlib one sns.set() # use the prettier seaborn plotting settings rather than the default matplotlib one
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
> We will mostly be using `seaborn` instead of `matplotlib` for > We will mostly be using `seaborn` instead of `matplotlib` for
> visualisation. But `seaborn` is actually an extension to `matplotlib`, so we > visualisation. But `seaborn` is actually an extension to `matplotlib`, so we
> are still using the latter under the hood. > are still using the latter under the hood.
## Loading in data ## Loading in data
Pandas supports a wide range of I/O tools to load from text files, binary files, Pandas supports a wide range of I/O tools to load from text files, binary files,
and SQL databases. You can find a table with all supported formats and SQL databases. You can find a table with all supported formats
[here](http://pandas.pydata.org/pandas-docs/stable/io.html). [here](http://pandas.pydata.org/pandas-docs/stable/io.html).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic = pd.read_csv('https://raw.githubusercontent.com/mwaskom/seaborn-data/master/titanic.csv') titanic = pd.read_csv('https://raw.githubusercontent.com/mwaskom/seaborn-data/master/titanic.csv')
titanic titanic
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
This loads the data into a This loads the data into a
[`DataFrame`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html) [`DataFrame`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html)
object, which is the main object we will be interacting with in pandas. It object, which is the main object we will be interacting with in pandas. It
represents a table of data. The input functions for other file formats all look like represents a table of data. The input functions for other file formats all look like
`pd.read_{format}`. Note that we can provide the URL to the dataset, without having `pd.read_{format}`. Note that we can provide the URL to the dataset, without having
to download it beforehand. to download it beforehand.
We can write out the dataset using `<dataframe>.to_{format}(<filename>)`: We can write out the dataset using `<dataframe>.to_{format}(<filename>)`:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.to_csv('titanic_copy.csv', index=False) # we set index to False to prevent pandas from storing the row indices (explained in more detail below) titanic.to_csv('titanic_copy.csv', index=False) # we set index to False to prevent pandas from storing the row indices (explained in more detail below)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
If you can not connect to the internet, you can run the command below to load If you can not connect to the internet, you can run the command below to load
this locally stored titanic dataset this locally stored titanic dataset
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic = pd.read_csv('titanic.csv') titanic = pd.read_csv('titanic.csv')
titanic titanic
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that the titanic dataset was also available to us as one of the standard Note that the titanic dataset was also available to us as one of the standard
datasets included with seaborn. We could load it from there using datasets included with seaborn. We could load it from there using
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.load_dataset('titanic') sns.load_dataset('titanic')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
`Dataframes` can also be created from other python objects, using `Dataframes` can also be created from other python objects, using
`pd.DataFrame.from_{other type}`. The most useful of these is `from_dict`, `pd.DataFrame.from_{other type}`. The most useful of these is `from_dict`,
which converts a mapping of the columns to a pandas `DataFrame` (i.e., table). which converts a mapping of the columns to a pandas `DataFrame` (i.e., table).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
pd.DataFrame.from_dict({ pd.DataFrame.from_dict({
'random numbers': np.random.rand(5), 'random numbers': np.random.rand(5),
'sequence (int)': np.arange(5), 'sequence (int)': np.arange(5),
'sequence (float)': np.linspace(0, 5, 5), 'sequence (float)': np.linspace(0, 5, 5),
'letters': list('abcde'), 'letters': list('abcde'),
'constant_value': 'same_value' 'constant_value': 'same_value'
}) })
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Getting your data out ## Getting your data out
For many applications (e.g., ICA, machine learning) you might want to For many applications (e.g., ICA, machine learning) you might want to
extract your data as a numpy array, even though more and more projects extract your data as a numpy array, even though more and more projects
support pandas Dataframes directly. The underlying numpy array can be support pandas Dataframes directly. The underlying numpy array can be
accessed using the `to_numpy` method accessed using the `to_numpy` method
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.to_numpy() titanic.to_numpy()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that the type of the returned array is the most common type (in this case Note that the type of the returned array is the most common type (in this case
object). If you just want the numeric parts of the table you can use object). If you just want the numeric parts of the table you can use
`select_dtypes`, which selects specific columns based on their dtype: `select_dtypes`, which selects specific columns based on their dtype:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.select_dtypes(include=np.number).to_numpy() titanic.select_dtypes(include=np.number).to_numpy()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that the numpy array has no information on the column names or row indices. Note that the numpy array has no information on the column names or row indices.
Alternatively, when you want to include the categorical variables in your later Alternatively, when you want to include the categorical variables in your later
analysis (e.g., for machine learning), you can extract dummy variables using: analysis (e.g., for machine learning), you can extract dummy variables using:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
pd.get_dummies(titanic) pd.get_dummies(titanic)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Accessing parts of the data ## Accessing parts of the data
[Documentation on indexing](http://pandas.pydata.org/pandas-docs/stable/indexing.html) [Documentation on indexing](http://pandas.pydata.org/pandas-docs/stable/indexing.html)
### Selecting columns by name ### Selecting columns by name
Single columns can be selected using the normal python indexing: Single columns can be selected using the normal python indexing:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic['embark_town'] titanic['embark_town']
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
If the column names is a valid python identifier (i.e., is a string that does not contain stuff like spaces) If the column names is a valid python identifier (i.e., is a string that does not contain stuff like spaces)
we can also access it as an attribute we can also access it as an attribute
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.embark_town titanic.embark_town
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that this returns a single column is represented by a pandas Note that this returns a single column is represented by a pandas
[`Series`](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html) [`Series`](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html)
rather than a `DataFrame` object. A `Series` is a 1-dimensional array rather than a `DataFrame` object. A `Series` is a 1-dimensional array
representing a single column, while a `DataFrame` is a collection of `Series` representing a single column, while a `DataFrame` is a collection of `Series`
representing a table. Multiple columns can be returned by providing a representing a table. Multiple columns can be returned by providing a
list of columns names. This will return a `DataFrame`: list of columns names. This will return a `DataFrame`:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic[['class', 'alive']] titanic[['class', 'alive']]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that you have to provide a list here (square brackets). If you provide a Note that you have to provide a list here (square brackets). If you provide a
tuple (round brackets) pandas will think you are trying to access a single tuple (round brackets) pandas will think you are trying to access a single
column that has that tuple as a name: column that has that tuple as a name:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic[('class', 'alive')] titanic[('class', 'alive')]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
In this case there is no column called `('class', 'alive')` leading to an In this case there is no column called `('class', 'alive')` leading to an
error. Later on we will see some uses to having columns named like this. error. Later on we will see some uses to having columns named like this.
The same interface can be used to add a new column (or updating an existing one): The same interface can be used to add a new column (or updating an existing one):
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic["my_column"] = 10 titanic["my_column"] = 10
titanic titanic
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can delete a column using: We can delete a column using:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
del titanic["my_column"] del titanic["my_column"]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Indexing rows by name or integer ### Indexing rows by name or integer
Individual rows can be accessed based on their name (i.e., the index) or integer Individual rows can be accessed based on their name (i.e., the index) or integer
(i.e., which row it is in). In our current table this will give the same (i.e., which row it is in). In our current table this will give the same
results. To ensure that these are different, let's sort our titanic dataset results. To ensure that these are different, let's sort our titanic dataset
based on the passenger fare: based on the passenger fare:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted = titanic.sort_values('fare') titanic_sorted = titanic.sort_values('fare')
titanic_sorted titanic_sorted
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that the re-sorting did not change the values in the index (i.e., left-most Note that the re-sorting did not change the values in the index (i.e., left-most
column). column).
We can select the first row of this newly sorted table using `iloc` We can select the first row of this newly sorted table using `iloc`
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.iloc[0] titanic_sorted.iloc[0]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can select the row with the index 0 using We can select the row with the index 0 using
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.loc[0] titanic_sorted.loc[0]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that this gives the same passenger as the first row of the initial table Note that this gives the same passenger as the first row of the initial table
before sorting before sorting
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.iloc[0] titanic.iloc[0]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Another common way to access the first or last N rows of a table is using the Another common way to access the first or last N rows of a table is using the
head/tail methods head/tail methods
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.head(3) titanic_sorted.head(3)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.tail(3) titanic_sorted.tail(3)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that nearly all methods in pandas return a new `DataFrame`, which means Note that nearly all methods in pandas return a new `DataFrame`, which means
that we can "chain" methods. What we mean by "chaining" is that rather than that we can "chain" methods. What we mean by "chaining" is that rather than
storing a returned `DataFrame`, we instead call a different method on it. storing a returned `DataFrame`, we instead call a different method on it.
For example, below the `tail` method call returns a new `DataFrame` For example, below the `tail` method call returns a new `DataFrame`
on which we then call the `head` method: on which we then call the `head` method:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.tail(10).head(5) # select the first 5 of the last 10 passengers in the database titanic_sorted.tail(10).head(5) # select the first 5 of the last 10 passengers in the database
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
> This chaining is usually very efficient, because when creating a new `DataFrame` > This chaining is usually very efficient, because when creating a new `DataFrame`
> pandas minimizes the copying of the underlying data (similar to what `numpy` arrays do). > pandas minimizes the copying of the underlying data (similar to what `numpy` arrays do).
> While this allows for fast manipulation of the data, it does mean that if you update the > While this allows for fast manipulation of the data, it does mean that if you update the
> data in one of your `DataFrame` the data *might* also be changed in related `DataFrame`s > data in one of your `DataFrame` the data *might* also be changed in related `DataFrame`s
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic_sorted.iloc[-10:-5] # alternative way to get the same passengers titanic_sorted.iloc[-10:-5] # alternative way to get the same passengers
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
**Exercise**: use sorting and tail/head or indexing to find the 10 youngest **Exercise**: use sorting and tail/head or indexing to find the 10 youngest
passengers on the titanic. Try to do this on a single line by chaining calls passengers on the titanic. Try to do this on a single line by chaining calls
to the titanic `DataFrame` object to the titanic `DataFrame` object
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.sort_values... titanic.sort_values...
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Indexing rows by value ### Indexing rows by value
One very common way to select specific columns is by their value One very common way to select specific columns is by their value
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic[titanic.sex == 'female'] # selects all females titanic[titanic.sex == 'female'] # selects all females
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
# select all passengers older than 60 who departed from Southampton # select all passengers older than 60 who departed from Southampton
titanic[(titanic.age > 60) & (titanic['embark_town'] == 'Southampton')] titanic[(titanic.age > 60) & (titanic['embark_town'] == 'Southampton')]
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that this required typing `titanic` quite often. Note that this required typing `titanic` quite often.
The `query` method allows you to get the same result with much less The `query` method allows you to get the same result with much less
typing (see [documentation](http://pandas.pydata.org/pandas-docs/stable/indexing.html#the-query-method)) typing (see [documentation](http://pandas.pydata.org/pandas-docs/stable/indexing.html#the-query-method))
(note that using the `query` method is also faster and uses a lot less (note that using the `query` method is also faster and uses a lot less
memory). memory).
> You may have trouble using the `query` method with columns which have > You may have trouble using the `query` method with columns which have
> a name that cannot be used as a Python identifier. > a name that cannot be used as a Python identifier.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.query('(age > 60) & (embark_town == "Southampton")') titanic.query('(age > 60) & (embark_town == "Southampton")')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
When selecting a categorical multiple options from a categorical values you When selecting a categorical multiple options from a categorical values you
might want to use `isin`: might want to use `isin`:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic[titanic['class'].isin(['First','Second'])] # select all passangers not in first or second class titanic[titanic['class'].isin(['First','Second'])] # select all passangers not in first or second class
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Particularly useful when selecting data like this is the `isna` method which Particularly useful when selecting data like this is the `isna` method which
finds all missing data finds all missing data
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic[~titanic.age.isna()] # select all passengers whose age is not N/A titanic[~titanic.age.isna()] # select all passengers whose age is not N/A
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
This removing of missing numbers is so common that it has is own method This removing of missing numbers is so common that it has is own method
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.dropna() # drops all passengers that have some datapoint missing titanic.dropna() # drops all passengers that have some datapoint missing
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.dropna(subset=['age', 'fare']) # Only drop passengers with missing ages or fares titanic.dropna(subset=['age', 'fare']) # Only drop passengers with missing ages or fares
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
**Exercise**: use sorting, indexing by value, `dropna` and `tail`/`head` or **Exercise**: use sorting, indexing by value, `dropna` and `tail`/`head` or
indexing to find the 10 oldest female passengers on the titanic. Try to do indexing to find the 10 oldest female passengers on the titanic. Try to do
this on a single line by chaining calls to the titanic `DataFrame` object this on a single line by chaining calls to the titanic `DataFrame` object
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic... titanic...
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Plotting the data ## Plotting the data
Before we start analyzing the data, let's play around with visualizing it. Before we start analyzing the data, let's play around with visualizing it.
Pandas does have some basic built-in plotting options: Pandas does have some basic built-in plotting options:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.fare.hist(bins=20, log=True) titanic.fare.hist(bins=20, log=True)
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.age.plot() titanic.age.plot()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
To plot all variables simply call `plot` or `hist` on the full `DataFrame` To plot all variables simply call `plot` or `hist` on the full `DataFrame`
rather than a single `Series` (i.e., column). You might want to set `subplots=True` rather than a single `Series` (i.e., column). You might want to set `subplots=True`
to plot each variable in a different subplot. to plot each variable in a different subplot.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.plot(subplots=True) titanic.plot(subplots=True)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Individual `Series` are essentially 1D arrays, so we can use them as such in Individual `Series` are essentially 1D arrays, so we can use them as such in
`matplotlib` `matplotlib`
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
plt.scatter(titanic.age, titanic.fare) plt.scatter(titanic.age, titanic.fare)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
However, for most purposes much nicer plots can be obtained using However, for most purposes much nicer plots can be obtained using
[Seaborn](https://seaborn.pydata.org). Seaborn has support to produce plots [Seaborn](https://seaborn.pydata.org). Seaborn has support to produce plots
showing the showing the
[univariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-univariate-distributions) [univariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-univariate-distributions)
or or
[bivariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-bivariate-distributions) [bivariate](https://seaborn.pydata.org/tutorial/distributions.html#plotting-bivariate-distributions)
distribution of data in a single or a grid of plots. Most of the seaborn distribution of data in a single or a grid of plots. Most of the seaborn
plotting functions expect to get a pandas `DataFrame` (although they will work plotting functions expect to get a pandas `DataFrame` (although they will work
with Numpy arrays as well). So we can plot age vs. fare like: with Numpy arrays as well). So we can plot age vs. fare like:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.jointplot('age', 'fare', data=titanic) sns.jointplot('age', 'fare', data=titanic)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
**Exercise**: check the documentation from `sns.jointplot` (hover the mouse **Exercise**: check the documentation from `sns.jointplot` (hover the mouse
over the text `jointplot` and press shift-tab) to find out how to turn the over the text `jointplot` and press shift-tab) to find out how to turn the
scatter plot into a density (kde) map scatter plot into a density (kde) map
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.jointplot('age', 'fare', data=titanic, ...) sns.jointplot('age', 'fare', data=titanic, ...)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Here is just a brief example of how we can use multiple columns to illustrate Here is just a brief example of how we can use multiple columns to illustrate
the data in more detail the data in more detail
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic, sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic,
col_order=('First', 'Second', 'Third')) col_order=('First', 'Second', 'Third'))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
**Exercise**: Split the plot above into two rows with the first row including **Exercise**: Split the plot above into two rows with the first row including
the passengers who survived and the second row those who did not (you might the passengers who survived and the second row those who did not (you might
have to check the documentation again by using shift-tab while hovering the have to check the documentation again by using shift-tab while hovering the
mouse over `relplot`) mouse over `relplot`)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic, sns.relplot(x='age', y='fare', col='class', hue='sex', data=titanic,
col_order=('First', 'Second', 'Third')...) col_order=('First', 'Second', 'Third')...)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
One of the nice thing of Seaborn is how easy it is to update how these plots One of the nice thing of Seaborn is how easy it is to update how these plots
look. You can read more about that look. You can read more about that
[here](https://seaborn.pydata.org/tutorial/aesthetics.html). For example, to [here](https://seaborn.pydata.org/tutorial/aesthetics.html). For example, to
increase the font size to get a plot more approriate for a talk, you can use: increase the font size to get a plot more approriate for a talk, you can use:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.set_context('talk') sns.set_context('talk')
sns.violinplot(x='class', y='age', hue='sex', data=titanic, split=True, sns.violinplot(x='class', y='age', hue='sex', data=titanic, split=True,
order=('First', 'Second', 'Third')) order=('First', 'Second', 'Third'))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Summarizing the data (mean, std, etc.) ## Summarizing the data (mean, std, etc.)
There are a large number of built-in methods to summarize the observations in There are a large number of built-in methods to summarize the observations in
a Pandas `DataFrame`. Most of these will return a `Series` with the columns a Pandas `DataFrame`. Most of these will return a `Series` with the columns
names as index: names as index:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.mean() titanic.mean()
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.quantile(0.75) titanic.quantile(0.75)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
One very useful one is `describe`, which gives an overview of many common One very useful one is `describe`, which gives an overview of many common
summary measures summary measures
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.describe() titanic.describe()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that non-numeric columns are ignored when summarizing data in this way. Note that non-numeric columns are ignored when summarizing data in this way.
For a more detailed exploration of the data, you might want to check For a more detailed exploration of the data, you might want to check
[pandas_profiling](https://pandas-profiling.github.io/pandas-profiling/docs/) [pandas_profiling](https://pandas-profiling.github.io/pandas-profiling/docs/)
(not installed in fslpython, so the following will not run in fslpython): (not installed in fslpython, so the following will not run in fslpython):
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
from pandas_profiling import ProfileReport from pandas_profiling import ProfileReport
profile = ProfileReport(titanic, title='Titanic Report', html={'style':{'full_width':True}}) profile = ProfileReport(titanic, title='Titanic Report', html={'style':{'full_width':True}})
profile.to_widgets() profile.to_widgets()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can also define our own functions to apply to the columns (in this case we We can also define our own functions to apply to the columns (in this case we
have to explicitly select the numeric columns). have to explicitly select the numeric columns).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
def mad(series): def mad(series):
""" """
Computes the median absolute deviatation (MAD) Computes the median absolute deviatation (MAD)
This is a outlier-resistant measure of the standard deviation This is a outlier-resistant measure of the standard deviation
""" """
no_nan = series.dropna() no_nan = series.dropna()
return np.median(abs(no_nan - np.nanmedian(no_nan))) return np.median(abs(no_nan - np.nanmedian(no_nan)))
titanic.select_dtypes(np.number).apply(mad) titanic.select_dtypes(np.number).apply(mad)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can also provide multiple functions to the `apply` method (note that We can also provide multiple functions to the `apply` method (note that
functions can be provided as strings) functions can be provided as strings)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.select_dtypes(np.number).apply(['mean', np.median, np.std, mad]) titanic.select_dtypes(np.number).apply(['mean', np.median, np.std, mad])
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
### Grouping by ### Grouping by
One of the more powerful features in pandas is `groupby`, which splits the dataset based One of the more powerful features in pandas is `groupby`, which splits the dataset based
on a categorical variable. The book contains a clear tutorial on that feature on a categorical variable. The book contains a clear tutorial on that feature
[here](https://jakevdp.github.io/PythonDataScienceHandbook/03.08-aggregation-and-grouping.html). You [here](https://jakevdp.github.io/PythonDataScienceHandbook/03.08-aggregation-and-grouping.html). You
can check the pandas documentation can check the pandas documentation
[here](http://pandas.pydata.org/pandas-docs/stable/groupby.html) for a more [here](http://pandas.pydata.org/pandas-docs/stable/groupby.html) for a more
formal introduction. One simple use is just to put it into a loop formal introduction. One simple use is just to put it into a loop
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
for cls, part_table in titanic.groupby('class'): for cls, part_table in titanic.groupby('class'):
print(f'Mean fare in {cls.lower()} class: {part_table.fare.mean()}') print(f'Mean fare in {cls.lower()} class: {part_table.fare.mean()}')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
However, it is more often combined with one of the aggregation functions However, it is more often combined with one of the aggregation functions
discussed above as illustrated in this figure from the [Python data science discussed above as illustrated in this figure from the [Python data science
handbook](https://jakevdp.github.io/PythonDataScienceHandbook/06.00-figure-code.html#Split-Apply-Combine) handbook](https://jakevdp.github.io/PythonDataScienceHandbook/06.00-figure-code.html#Split-Apply-Combine)
![group by image](group_by.png) ![group by image](group_by.png)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby('class').mean() titanic.groupby('class').mean()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can also group by multiple variables at once We can also group by multiple variables at once
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby(['class', 'survived']).mean() # as always in pandas supply multiple column names as lists, not tuples titanic.groupby(['class', 'survived']).mean() # as always in pandas supply multiple column names as lists, not tuples
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
When grouping it can help to use the `cut` method to split a continuous variable When grouping it can help to use the `cut` method to split a continuous variable
into a categorical one into a categorical one
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby(['class', pd.cut(titanic.age, bins=(0, 18, 50, np.inf))]).mean() titanic.groupby(['class', pd.cut(titanic.age, bins=(0, 18, 50, np.inf))]).mean()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can use the `aggregate` method to apply a different function to each series We can use the `aggregate` method to apply a different function to each series
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby(['class', 'survived']).aggregate((np.median, mad)) titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that both the index (on the left) and the column names (on the top) now Note that both the index (on the left) and the column names (on the top) now
have multiple levels. Such an index is referred to as `MultiIndex`. have multiple levels. Such an index is referred to as `MultiIndex`.
This does complicate selecting specific columns/rows. You can read more of using This does complicate selecting specific columns/rows. You can read more of using
`MultiIndex` [here](http://pandas.pydata.org/pandas-docs/stable/advanced.html). `MultiIndex` [here](http://pandas.pydata.org/pandas-docs/stable/advanced.html).
The short version is that columns can be selected using direct indexing (as The short version is that columns can be selected using direct indexing (as
discussed above) discussed above)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, mad)) df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full[('age', 'median')] # selects median age column; note that the round brackets are optional df_full[('age', 'median')] # selects median age column; note that the round brackets are optional
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full['age'] # selects both age columns df_full['age'] # selects both age columns
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Remember that indexing based on the index was done through `loc`. The rest is Remember that indexing based on the index was done through `loc`. The rest is
the same as for the columns above the same as for the columns above
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full.loc[('First', 0)] df_full.loc[('First', 0)]
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full.loc['First'] df_full.loc['First']
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
More advanced use of the `MultiIndex` is possible through `xs`: More advanced use of the `MultiIndex` is possible through `xs`:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full.xs(0, level='survived') # selects all the zero's from the survived index df_full.xs(0, level='survived') # selects all the zero's from the survived index
``` ```
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_full.xs('mad', axis=1, level=1) # selects mad from the second level in the columns (i.e., axis=1) df_full.xs('mad', axis=1, level=1) # selects mad from the second level in the columns (i.e., axis=1)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Reshaping tables ## Reshaping tables
If we were interested in how the survival rate depends on the class and sex of If we were interested in how the survival rate depends on the class and sex of
the passengers we could simply use a groupby: the passengers we could simply use a groupby:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby(['class', 'sex']).survived.mean() titanic.groupby(['class', 'sex']).survived.mean()
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
However, this single-column table is difficult to read. The reason for this is However, this single-column table is difficult to read. The reason for this is
that the indexing is multi-leveled (called `MultiIndex` in pandas), while there that the indexing is multi-leveled (called `MultiIndex` in pandas), while there
is only a single column. We would like to move one of the levels in the index to is only a single column. We would like to move one of the levels in the index to
the columns. This can be done using `stack`/`unstack`: the columns. This can be done using `stack`/`unstack`:
- `unstack`: Moves one level in the index to the columns - `unstack`: Moves one level in the index to the columns
- `stack`: Moves one level in the columns to the index - `stack`: Moves one level in the columns to the index
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.groupby(['class', 'sex']).survived.mean().unstack('sex') titanic.groupby(['class', 'sex']).survived.mean().unstack('sex')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
The former table, where the different groups are defined in different rows, is The former table, where the different groups are defined in different rows, is
often referred to as long-form. After unstacking the table is often referred to often referred to as long-form. After unstacking the table is often referred to
as wide-form as the different groups (sex in this case) is now represented as as wide-form as the different groups (sex in this case) is now represented as
different columns. In pandas some operations are easier on long-form tables different columns. In pandas some operations are easier on long-form tables
(e.g., `groupby`) while others require wide_form tables (e.g., making scatter (e.g., `groupby`) while others require wide_form tables (e.g., making scatter
plots of two variables). You can go back and forth using `unstack` or `stack` as plots of two variables). You can go back and forth using `unstack` or `stack` as
illustrated above, but as this is a crucial part of pandas there are many illustrated above, but as this is a crucial part of pandas there are many
alternatives, such as `pivot_table`, `melt`, and `wide_to_long`, which we will alternatives, such as `pivot_table`, `melt`, and `wide_to_long`, which we will
discuss below. discuss below.
We can prettify the table further using seaborn We can prettify the table further using seaborn
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
ax = sns.heatmap(titanic.groupby(['class', 'sex']).survived.mean().unstack('sex'), ax = sns.heatmap(titanic.groupby(['class', 'sex']).survived.mean().unstack('sex'),
annot=True) annot=True)
ax.set_title('survival rate') ax.set_title('survival rate')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
> There are also many ways to produce prettier tables in pandas. > There are also many ways to produce prettier tables in pandas.
> This is documented [here](http://pandas.pydata.org/pandas-docs/stable/style.html). > This is documented [here](http://pandas.pydata.org/pandas-docs/stable/style.html).
Because this stacking/unstacking is fairly common after a groupby operation, Because this stacking/unstacking is fairly common after a groupby operation,
there is a shortcut for it: `pivot_table` there is a shortcut for it: `pivot_table`
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.pivot_table('survived', 'class', 'sex') titanic.pivot_table('survived', 'class', 'sex')
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
The first argument is the numeric variable that will be summarised. The first argument is the numeric variable that will be summarised.
The next arguments indicates which categorical variable(s) should be The next arguments indicates which categorical variable(s) should be
used as respectively index or column. used as respectively index or column.
As usual in pandas we can also provide multiple column names As usual in pandas we can also provide multiple column names
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))]), annot=True) sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))]), annot=True)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can also change the function to be used to aggregate the data (by default the mean is computed) We can also change the function to be used to aggregate the data (by default the mean is computed)
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))], sns.heatmap(titanic.pivot_table('survived', ['class', 'embark_town'], ['sex', pd.cut(titanic.age, (0, 18, np.inf))],
aggfunc='count'), annot=True) aggfunc='count'), annot=True)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
As in `groupby` the aggregation function can be a string of a common aggregation As in `groupby` the aggregation function can be a string of a common aggregation
function, or any function that should be applied. function, or any function that should be applied.
We can even apply different aggregate functions to different columns We can even apply different aggregate functions to different columns
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
titanic.pivot_table(index='class', columns='sex', titanic.pivot_table(index='class', columns='sex',
aggfunc={'survived': 'count', 'fare': np.mean}) # compute number of survivors and mean fare aggfunc={'survived': 'count', 'fare': np.mean}) # compute number of survivors and mean fare
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
The opposite of `pivot_table` is `melt`. This can be used to change a wide-form The opposite of `pivot_table` is `melt`. This can be used to change a wide-form
table into a long-form table. This is not particularly useful on the titanic table into a long-form table. This is not particularly useful on the titanic
dataset, so let's create a new table where this might be useful. Let's say we dataset, so let's create a new table where this might be useful. Let's say we
have a dataset listing the FA and MD values in various WM tracts: have a dataset listing the FA and MD values in various WM tracts:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
tracts = ('Corpus callosum', 'Internal capsule', 'SLF', 'Arcuate fasciculus') tracts = ('Corpus callosum', 'Internal capsule', 'SLF', 'Arcuate fasciculus')
df_wide = pd.DataFrame.from_dict(dict({'subject': list('ABCDEFGHIJ')}, **{ df_wide = pd.DataFrame.from_dict(dict({'subject': list('ABCDEFGHIJ')}, **{
f'FA({tract})': np.random.rand(10) for tract in tracts }, **{ f'FA({tract})': np.random.rand(10) for tract in tracts }, **{
f'MD({tract})': np.random.rand(10) * 1e-3 for tract in tracts f'MD({tract})': np.random.rand(10) * 1e-3 for tract in tracts
})) }))
df_wide df_wide
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
This wide-form table (i.e., all the information is in different columns) makes This wide-form table (i.e., all the information is in different columns) makes
it hard to select just all the FA values or only the values associated with the it hard to select just all the FA values or only the values associated with the
SLF. For this it would be easier to list all the values in a single column. SLF. For this it would be easier to list all the values in a single column.
Most of the tools discussed above (e.g., `group_by` or `seaborn` plotting) work Most of the tools discussed above (e.g., `group_by` or `seaborn` plotting) work
better with long-form data, which we can obtain from `melt`: better with long-form data, which we can obtain from `melt`:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_long = df_wide.melt('subject', var_name='measurement', value_name='dti_value') df_long = df_wide.melt('subject', var_name='measurement', value_name='dti_value')
df_long.head(12) df_long.head(12)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can see that `melt` took all the columns (we could also have specified a We can see that `melt` took all the columns (we could also have specified a
specific sub-set) and returned each measurement as a seperate row. We probably specific sub-set) and returned each measurement as a seperate row. We probably
want to seperate the measurement column into the measurement type (FA or MD) and want to seperate the measurement column into the measurement type (FA or MD) and
the tract name. Many string manipulation function are available in the the tract name. Many string manipulation function are available in the
`DataFrame` object under `DataFrame.str` `DataFrame` object under `DataFrame.str`
([tutorial](http://pandas.pydata.org/pandas-docs/stable/text.html)) ([tutorial](http://pandas.pydata.org/pandas-docs/stable/text.html))
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_long['variable'] = df_long.measurement.str.slice(0, 2) # first two letters correspond to FA or MD df_long['variable'] = df_long.measurement.str.slice(0, 2) # first two letters correspond to FA or MD
df_long['tract'] = df_long.measurement.str.slice(3, -1) # fourth till the second-to-last letter correspond to the tract df_long['tract'] = df_long.measurement.str.slice(3, -1) # fourth till the second-to-last letter correspond to the tract
df_long.head(12) df_long.head(12)
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Finally we probably do want the FA and MD variables as different columns. Finally we probably do want the FA and MD variables as different columns.
**Exercise**: Use `pivot_table` or `stack`/`unstack` to create a column for MD **Exercise**: Use `pivot_table` or `stack`/`unstack` to create a column for MD
and FA. and FA.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
df_unstacked = df_long. df_unstacked = df_long.
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
We can now use the tools discussed above to visualize the table (`seaborn`) or We can now use the tools discussed above to visualize the table (`seaborn`) or
to group the table based on tract (`groupby` or `pivot_table`). to group the table based on tract (`groupby` or `pivot_table`).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
# feel free to analyze this random data in more detail # feel free to analyze this random data in more detail
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
In general pandas is better at handling long-form than wide-form data, because In general pandas is better at handling long-form than wide-form data, because
you can use `groupby` on long-form data. you can use `groupby` on long-form data.
For better visualization of the data an intermediate format is often preferred. One For better visualization of the data an intermediate format is often preferred. One
exception is calculating a covariance (`DataFrame.cov`) or correlation exception is calculating a covariance (`DataFrame.cov`) or correlation
(`DataFrame.corr`) matrices which require the variables that will be compared (`DataFrame.corr`) matrices which require the variables that will be compared
to be columns: to be columns:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
sns.heatmap(df_wide.corr(), cmap=sns.diverging_palette(240, 10, s=99, n=300), ) sns.heatmap(df_wide.corr(), cmap=sns.diverging_palette(240, 10, s=99, n=300), )
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
## Linear fitting (`statsmodels`) ## Linear fitting (`statsmodels`)
Linear fitting between the different columns is available through the Linear fitting between the different columns is available through the
[`statsmodels`](https://www.statsmodels.org/stable/index.html) library. A nice [`statsmodels`](https://www.statsmodels.org/stable/index.html) library. A nice
way to play around with a wide variety of possible models is to use R-style way to play around with a wide variety of possible models is to use R-style
formulas. The usage of the formulas in `statsmodels` is described formulas. The usage of the formulas in `statsmodels` is described
[here](https://www.statsmodels.org/dev/example_formulas.html). You can find a [here](https://www.statsmodels.org/dev/example_formulas.html). You can find a
more detailed description of the R-style formulas more detailed description of the R-style formulas
[here](https://patsy.readthedocs.io/en/latest/formulas.html#the-formula-language). [here](https://patsy.readthedocs.io/en/latest/formulas.html#the-formula-language).
In short these functions describe the linear model as a string. For example, In short these functions describe the linear model as a string. For example,
`"y ~ x + a + x * a"` fits the variable `y` as a function of `x`, `a`, and the `"y ~ x + a + x * a"` fits the variable `y` as a function of `x`, `a`, and the
interaction between `x` and `a`. The intercept parameter is included by default interaction between `x` and `a`. The intercept parameter is included by default
(you can add `"+ 0"` to remove it). (you can add `"+ 0"` to remove it).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
result = smf.logit('survived ~ age + sex + age * sex', data=titanic).fit() result = smf.logit('survived ~ age + sex + age * sex', data=titanic).fit()
print(result.summary()) print(result.summary())
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Note that `statsmodels` understands categorical variables and automatically Note that `statsmodels` understands categorical variables and automatically
replaces them with dummy variables. replaces them with dummy variables.
Above we used logistic regression, which is appropriate for the binary Above we used logistic regression, which is appropriate for the binary
survival rate. A wide variety of linear models are available. Let's try a GLM, survival rate. A wide variety of linear models are available. Let's try a GLM,
but assume that the fare is drawn from a Gamma distribution: but assume that the fare is drawn from a Gamma distribution:
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` ```
age_dmean = titanic.age - titanic.age.mean() age_dmean = titanic.age - titanic.age.mean()
result = smf.glm('fare ~ age_dmean + embark_town', data=titanic).fit() result = smf.glm('fare ~ age_dmean + embark_town', data=titanic).fit()
print(result.summary()) print(result.summary())
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Cherbourg passengers clearly paid a lot more... Cherbourg passengers clearly paid a lot more...
Note that we did not actually add the "age_dmean" `Series` to the Note that we did not actually add the "age_dmean" `Series` to the
`DataFrame`. `statsmodels` (or more precisely the underlying `DataFrame`. `statsmodels` (or more precisely the underlying
[patsy](https://patsy.readthedocs.io/en/latest/) library) automatically [patsy](https://patsy.readthedocs.io/en/latest/) library) automatically
extracted this from our environment. This can lead to confusing behaviour... extracted this from our environment. This can lead to confusing behaviour...
# More reading # More reading
If you regularly keep running out of memory when handling large tables (e.g., Biobank), you should consider using [dask DataFrames](https://docs.dask.org/en/latest/dataframe.html) instead. They have the same interface as `pandas` `DataFrame`, but will split up your instructions into smaller jobs that can run without the full table being loaded into memory. Many other options for out-of-core computation are listed [here](https://pandas.pydata.org/docs/ecosystem.html#out-of-core). If you regularly keep running out of memory when handling large tables (e.g., Biobank), you should consider using [dask DataFrames](https://docs.dask.org/en/latest/dataframe.html) instead. They have the same interface as `pandas` `DataFrame`, but will split up your instructions into smaller jobs that can run without the full table being loaded into memory. Many other options for out-of-core computation are listed [here](https://pandas.pydata.org/docs/ecosystem.html#out-of-core).
Not all data is well represented by a 2D table. If you want more dimensions to for example represent MRI data, have a look at [xarray](https://github.com/pydata/xarray), which has a pandas-like interface for higher-dimensional objects. Not all data is well represented by a 2D table. If you want more dimensions to for example represent MRI data, have a look at [xarray](https://github.com/pydata/xarray), which has a pandas-like interface for higher-dimensional objects.
Other useful features: Other useful features:
- [Concatenating and merging tables](https://pandas.pydata.org/pandas-docs/stable/getting_started/intro_tutorials/08_combine_dataframes.html) - [Concatenating and merging tables](https://pandas.pydata.org/pandas-docs/stable/getting_started/intro_tutorials/08_combine_dataframes.html)
- [Lots of time series support](https://pandas.pydata.org/pandas-docs/stable/getting_started/intro_tutorials/09_timeseries.html) - [Lots of time series support](https://pandas.pydata.org/pandas-docs/stable/getting_started/intro_tutorials/09_timeseries.html)
- [Rolling Window - [Rolling Window
functions](http://pandas.pydata.org/pandas-docs/stable/computation.html#window- functions](http://pandas.pydata.org/pandas-docs/stable/computation.html#window-
functions) for after you have meaningfully sorted your data functions) for after you have meaningfully sorted your data
- and much, much more - and much, much more
......
...@@ -462,7 +462,7 @@ titanic.groupby(['class', pd.cut(titanic.age, bins=(0, 18, 50, np.inf))]).mean() ...@@ -462,7 +462,7 @@ titanic.groupby(['class', pd.cut(titanic.age, bins=(0, 18, 50, np.inf))]).mean()
We can use the `aggregate` method to apply a different function to each series We can use the `aggregate` method to apply a different function to each series
``` ```
titanic.groupby(['class', 'survived']).aggregate((np.median, mad)) titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))
``` ```
Note that both the index (on the left) and the column names (on the top) now Note that both the index (on the left) and the column names (on the top) now
...@@ -473,7 +473,7 @@ The short version is that columns can be selected using direct indexing (as ...@@ -473,7 +473,7 @@ The short version is that columns can be selected using direct indexing (as
discussed above) discussed above)
``` ```
df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, mad)) df_full = titanic.groupby(['class', 'survived']).aggregate((np.median, 'mad'))
``` ```
``` ```
......
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