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Matplotlib marker module is a wonderful multi-platform data visualization library in python used to plot 2D arrays and vectors. Matplotlib is designed to work with the broader SciPy stack. Matplotlib is designed to work with the broader SciPy stack. When creating a figure with multiple plots, users often want one title centered over all plots instead of individual titles. The plot is what happens in a story. However, a plot is not a simple sequence of events. A strong plot is centered on one moment—an interruption of a pattern, a turning point, or an action—that raises a dramatic question, which must be answered throughout the course of the story. This is also known as plot A. Centered on the theme of marriage with intertwining plots 4. Centered on a major flaw in the main character's personality 5. Based on the dramatization of significant historical events. Answers (1) Tibelda 10 September, 16:16. Centered on the theme of marriage with intertwining plots.

Plot likert scales as centered stacked bars

Plot likert scales as centered stacked bars.

Arguments

Data frame, or a grouped data frame, with each column representing one item.

(optional) Must be a vector of same length as ncol(items),where each item in this vector represents the group numberof the related columns of items. See 'Examples'.

(optional, only used if groups are supplied) Titles for each factor group that will be used as table caption for eachcomponent-table. Must be a character vector of same length as length(unique(groups)).Default is 'auto', which means that each table has a standard caption Component x.Use NULL to use names as supplied to groups and use FALSE to suppress table captions.

character vector, used as plot title. Depending on plot type and function,will be set automatically. If title = ', no title is printed.For effect-plots, may also be a character vector of length > 1,to define titles for each sub-plot or facet.

character vector, used as title for the plot legend.

character vector with labels for the guide/legend.

character vector of length one or two, defining the title(s)for the x-axis and y-axis.

character vector with labels used as axis labels. Optionalargument, since in most cases, axis labels are set automatically.

optional, amount of categories of items (e.g. 'strongly disagree','disagree', 'agree' and 'strongly agree' would be catcount = 4).Note that this argument only applies to 'valid' answers, i.e. if youhave an additional neutral category (see cat.neutral) like 'don't know',this won't count for catcount (e.g. 'strongly disagree','disagree', 'agree', 'strongly agree' and neutral category 'don't know'would still mean that catcount = 4). See 'Note'.

If there's a neutral category (like 'don't know' etc.), specifythe index number (value) for this category. Else, set cat.neutral = NULL (default).The proportions of neutral category answers are plotted as grey bars on the left side ofthe figure.

Indicates whether the items of items should be ordered bytotal sum of positive or negative answers.

to order ascending by sum of positive answers

to order descending by sum of positive answers

for sorting ascending negative answers

for sorting descending negative answers

(default) for no sorting

Vector of weights that will be applied to weight all cases.Must be a vector of same length as the input vector. Default isNULL, so no weights are used.

Suffix (as string) for the title, if weight.by is specified,e.g. title.wtd.suffix=' (weighted)'. Default is NULL, sotitle will not have a suffix when cases are weighted.

numeric, determines how many chars of the plot title are displayed inone line and when a line break is inserted.

numeric, determines how many chars of the value, variable or axislabels are displayed in one line and when a line break is inserted.

numeric, determines how many chars of the legend's titleare displayed in one line and when a line break is inserted.

numeric, determines how many chars of the legend labels aredisplayed in one line and when a line break is inserted.

size resp. width of the geoms (bar width, line thickness or point size,depending on plot type and function). Note that bar and bin widths mostlyneed smaller values than dot sizes.

user defined color for geoms. See 'Details' in plot_grpfrq.

Color of the neutral category, if plotted (see cat.neutral).

Color of the vertical intercept line that divides positive and negative values.

logical, if TRUE, the color scale from geom.colors will be reversed,so positive and negative values switch colors.

Determines style and position of percentage value labels on the bars:

(default) shows percentage value labels in the middle of each category bar

hides the value labels, so no percentage values on the bars are printed

shows the sums of percentage values for both negative and positive values and prints them inside the end of each bar

shows the sums of percentage values for both negative and positive values and prints them outside the end of each bar

logical, if TRUE, adds total number of cases for eachgroup or category to the labels.

logical, if TRUE, and depending on plot type andfunction, a legend is added to the plot.

logical, if TRUE, %-signs for value labels are shown.

Numeric, limits of the x-axis-range, as proportion of 100.Default is 1, so the x-scale ranges from zero to 100% on both sides from the center.Can alternatively be supplied as a vector of 2 positive numbers (e.g. grid.range = c(1, .8))to set the left and right limit separately. You can use values beyond 1 (100%) in case bar labels are not printed becausethey exceed the axis range. E.g. grid.range = 1.4 will set the axis from -140 to +140%, however, only(valid) axis labels from -100 to +100% are printed. Neutral categories are adjusted to the most left limit.

numeric; sets the distance between breaks for the axis,i.e. at every grid.breaks'th position a major grid is being printed.

logical, if TRUE, the plot grid is expanded, i.e. there is a small margin betweenaxes and plotting region. Default is FALSE.

Numeric, amount of digits after decimal point when roundingestimates or values.

logical, if TRUE, the ordering of the categories is reversed, so positive and negative values switch position.

logical, if TRUE, the x and y axis are swapped.

(optional, only used if groups are supplied) logical, if groups should be sorted according to the values supplied to groups. Defaults to TRUE.

(optional, only used if groups are supplied) Defines the legend position. Possible values are c('bottom', 'top', 'both', 'all', 'none').If the is only one group or this option is set to 'all' legends will be printed as defined with set_theme.

(optional, only used if groups are supplied) This option can be used to adjust the height of the subplots. The bars in subplots can have different heights due to a differing number of itemsor due to legend placement. This can be adjusted here. Takes a vector of numbers, onefor each plot. Values are evaluated relative to each other.

(optional, only used if groups are supplied) List of options to be passed to guide_legend.The most notable options are byrow=T (default), this will order the categories row wise.And with group.legend.options = list(nrow = 1) all categories can be forced to be on a single row.

(optional, only used if groups are supplied) List of label options to be passed to plot_grid.

Value

A ggplot-object.

Note

Note that only even numbers of categories are possible to plot, so the 'positive' and 'negative' values can be splitted into two halfs. A neutral category (like 'don't know') can be used, but must be indicated by cat.neutral. The catcount-argument indicates how many item categories are in the Likert scale. Normally, this argument can be ignored because the amount of valid categories is retrieved automatically. However, sometimes (for instance, if a certain category is missing in all items), auto-detection of the amount of categories fails. In such cases, specify the amount of categories with the catcount-argument.

Aliases

• plot_likert

Partial dependence plots (PDP) and individual conditional expectation (ICE)plots can be used to visualize and analyze interaction between the targetresponse 1 and a set of input features of interest.

Both PDPs and ICEs assume that the input features of interest are independentfrom the complement features, and this assumption is often violated in practice.Thus, in the case of correlated features, we will create absurd data points tocompute the PDP/ICE.

4.1.1. Partial dependence plots¶

Partial dependence plots (PDP) show the dependence between the target responseand a set of input features of interest, marginalizing over the valuesof all other input features (the ‘complement’ features). Intuitively, we caninterpret the partial dependence as the expected target response as afunction of the input features of interest.

Due to the limits of human perception the size of the set of input feature ofinterest must be small (usually, one or two) thus the input features of interestare usually chosen among the most important features.

The figure below shows two one-way and one two-way partial dependence plots forthe California housing dataset, with a HistGradientBoostingRegressor:

One-way PDPs tell us about the interaction between the target response and aninput feature of interest feature (e.g. linear, non-linear). The left plotin the above figure shows the effect of the average occupancy on the medianhouse price; we can clearly see a linear relationship among them when theaverage occupancy is inferior to 3 persons. Similarly, we could analyze theeffect of the house age on the median house price (middle plot). Thus, theseinterpretations are marginal, considering a feature at a time.

PDPs with two input features of interest show the interactions among the twofeatures. For example, the two-variable PDP in the above figure shows thedependence of median house price on joint values of house age and averageoccupants per household. We can clearly see an interaction between the twofeatures: for an average occupancy greater than two, the house price is nearlyindependent of the house age, whereas for values less than 2 there is a strongdependence on age.

The sklearn.inspection module provides a convenience functionplot_partial_dependence to create one-way and two-way partialdependence plots. In the below example we show how to create a grid ofpartial dependence plots: two one-way PDPs for the features 0 and 1and a two-way PDP between the two features:

You can access the newly created figure and Axes objects using plt.gcf()and plt.gca().

For multi-class classification, you need to set the class label for whichthe PDPs should be created via the target argument:

The same parameter target is used to specify the target in multi-outputregression settings.

If you need the raw values of the partial dependence function rather thanthe plots, you can use thesklearn.inspection.partial_dependence function:

The values at which the partial dependence should be evaluated are directlygenerated from X. For 2-way partial dependence, a 2D-grid of values isgenerated. The values field returned bysklearn.inspection.partial_dependence gives the actual valuesused in the grid for each input feature of interest. They also correspond tothe axis of the plots.

4.1.2. Individual conditional expectation (ICE) plot¶

Similar to a PDP, an individual conditional expectation (ICE) plotshows the dependence between the target function and an input feature ofinterest. However, unlike a PDP, which shows the average effect of the inputfeature, an ICE plot visualizes the dependence of the prediction on afeature for each sample separately with one line per sample.Due to the limits of human perception, only one input feature of interest issupported for ICE plots.

The figures below show four ICE plots for the California housing dataset,with a HistGradientBoostingRegressor. The second figure plotsthe corresponding PD line overlaid on ICE lines.

While the PDPs are good at showing the average effect of the target features,they can obscure a heterogeneous relationship created by interactions.When interactions are present the ICE plot will provide many more insights.For example, we could observe a linear relationship between the median incomeand the house price in the PD line. However, the ICE lines show that thereare some exceptions, where the house price remains constant in some ranges ofthe median income.

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The sklearn.inspection module’s plot_partial_dependenceconvenience function can be used to create ICE plots by settingkind='individual'. In the example below, we show how to create a grid ofICE plots:

In ICE plots it might not be easy to see the average effect of the inputfeature of interest. Hence, it is recommended to use ICE plots alongsidePDPs. They can be plotted together withkind='both'.

4.1.3. Mathematical Definition¶

Let (X_S) be the set of input features of interest (i.e. the featuresparameter) and let (X_C) be its complement.

The partial dependence of the response (f) at a point (x_S) isdefined as:

where (f(x_S, x_C)) is the response function (predict,predict_proba or decision_function) for a given sample whosevalues are defined by (x_S) for the features in (X_S), and by(x_C) for the features in (X_C). Note that (x_S) and(x_C) may be tuples.

Computing this integral for various values of (x_S) produces a PDP plotas above. An ICE line is defined as a single (f(x_{S}, x_{C}^{(i)}))evaluated at (x_{S}).

4.1.4. Computation methods¶

There are two main methods to approximate the integral above, namely the‘brute’ and ‘recursion’ methods. The method parameter controls which methodto use.

The ‘brute’ method is a generic method that works with any estimator. Note thatcomputing ICE plots is only supported with the ‘brute’ method. Itapproximates the above integral by computing an average over the data X:

where (x_C^{(i)}) is the value of the i-th sample for the features in(X_C). For each value of (x_S), this method requires a full passover the dataset X which is computationally intensive.

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Each of the (f(x_{S}, x_{C}^{(i)})) corresponds to one ICE line evaluatedat (x_{S}). Computing this for multiple values of (x_{S}), oneobtains a full ICE line. As one can see, the average of the ICE linescorrespond to the partial dependence line.

The ‘recursion’ method is faster than the ‘brute’ method, but it is onlysupported for PDP plots by some tree-based estimators. It is computed asfollows. For a given point (x_S), a weighted tree traversal is performed:if a split node involves an input feature of interest, the corresponding leftor right branch is followed; otherwise both branches are followed, each branchbeing weighted by the fraction of training samples that entered that branch.Finally, the partial dependence is given by a weighted average of all thevisited leaves values.

With the ‘brute’ method, the parameter X is used both for generating thegrid of values (x_S) and the complement feature values (x_C).However with the ‘recursion’ method, X is only used for the grid values:implicitly, the (x_C) values are those of the training data.

By default, the ‘recursion’ method is used for plotting PDPs on tree-basedestimators that support it, and ‘brute’ is used for the rest.

Note

While both methods should be close in general, they might differ in somespecific settings. The ‘brute’ method assumes the existence of thedata points ((x_S, x_C^{(i)})). When the features are correlated,such artificial samples may have a very low probability mass. The ‘brute’and ‘recursion’ methods will likely disagree regarding the value of thepartial dependence, because they will treat these unlikelysamples differently. Remember, however, that the primary assumption forinterpreting PDPs is that the features should be independent.

Examples:

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Footnotes

For classification, the target response may be the probability of aclass (the positive class for binary classification), or the decisionfunction.

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References

Plots Centered Approach

T. Hastie, R. Tibshirani and J. Friedman, The Elements ofStatistical Learning,Second Edition, Section 10.13.2, Springer, 2009.

Plots Centered School

C. Molnar, Interpretable Machine Learning, Section 5.1, 2019.

A. Goldstein, A. Kapelner, J. Bleich, and E. Pitkin, Peeking Inside theBlack Box: Visualizing Statistical Learning With Plots of IndividualConditional Expectation,Journal of Computational and Graphical Statistics, 24(1): 44-65, Springer,2015.