econml.inference.NormalInferenceResults

class econml.inference.NormalInferenceResults(d_t, d_y, pred, pred_stderr, mean_pred_stderr, inf_type, fname_transformer=None, feature_names=None, output_names=None, treatment_names=None)

Bases: econml.inference._inference.InferenceResults

Results class for inference assuming a normal distribution.

Parameters

• d_t (int or None) – Number of treatments

• d_y (int) – Number of outputs

• pred (array_like, shape (m, d_y, d_t) or (m, d_y)) – The prediction of the metric for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions should be collapsed (e.g. if both are vectors, then the input of this argument will also be a vector)

• pred_stderr (array_like, shape (m, d_y, d_t) or (m, d_y)) – The prediction standard error of the metric for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions should be collapsed (e.g. if both are vectors, then the input of this argument will also be a vector)

• mean_pred_stderr (None or array_like or scaler, shape (d_y, d_t) or (d_y,)) – The standard error of the mean point estimate, this is derived from coefficient stderr when final stage is linear model, otherwise it’s None. This is the exact standard error of the mean, which is not conservative.

• inf_type (str) – The type of inference result. It could be either ‘effect’, ‘coefficient’ or ‘intercept’.

• fname_transformer (None or predefined function) – The transform function to get the corresponding feature names from featurizer

__init__(d_t, d_y, pred, pred_stderr, mean_pred_stderr, inf_type, fname_transformer=None, feature_names=None, output_names=None, treatment_names=None)

Methods

__init__(d_t, d_y, pred, pred_stderr, ...[, ...])
conf_int([alpha])	Get the confidence interval of the metric of each treatment on each outcome for each sample X[i].
population_summary([alpha, value, decimals, ...])	Output the object of population summary results.
pvalue([value])	Get the p value of the z test of each treatment on each outcome for each sample X[i].
scale(factor)	Update the results in place by scaling by a factor.
summary_frame([alpha, value, decimals, ...])	Output the dataframe for all the inferences above.
translate(offset)	Update the results in place by translating by an offset.
zstat([value])	Get the z statistic of the metric of each treatment on each outcome for each sample X[i].

Attributes

point_estimate	Get the point estimate of each treatment on each outcome for each sample X[i].
stderr	Get the standard error of the metric of each treatment on each outcome for each sample X[i].
var	Get the variance of the metric of each treatment on each outcome for each sample X[i].

conf_int(alpha=0.05)

Get the confidence interval of the metric of each treatment on each outcome for each sample X[i].

Parameters

alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1-alpha/2 confidence interval is reported.

Returns

lower, upper – The lower and the upper bounds of the confidence interval for each quantity. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

tuple of array, shape (m, d_y, d_t) or (m, d_y)

population_summary(alpha=0.05, value=0, decimals=3, tol=0.001, output_names=None, treatment_names=None)

Output the object of population summary results.

Parameters

• alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1-alpha/2 confidence interval is reported.

• value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.

• decimals (int, default 3) – Number of decimal places to round each column to.

• tol (float, default 0.001) – The stopping criterion. The iterations will stop when the outcome is less than tol

• output_names (list of str, optional) – The names of the outputs

• treatment_names (list of str, optional) – The names of the treatments

Returns

PopulationSummaryResults – The population summary results instance contains the different summary analysis of point estimate for sample X on each treatment and outcome.

Return type

object

pvalue(value=0)

Get the p value of the z test of each treatment on each outcome for each sample X[i].

Parameters

value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.

Returns

pvalue – The p value of the z test of each treatment on each outcome for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

array_like, shape (m, d_y, d_t) or (m, d_y)

scale(factor)

Update the results in place by scaling by a factor.

Parameters

factor (array_like) – The factor by which to scale these results

summary_frame(alpha=0.05, value=0, decimals=3, feature_names=None, output_names=None, treatment_names=None)

Output the dataframe for all the inferences above.

Parameters

• alpha (float in [0, 1], default 0.05) – The overall level of confidence of the reported interval. The alpha/2, 1-alpha/2 confidence interval is reported.

• value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.

• decimals (int, default 3) – Number of decimal places to round each column to.

• feature_names (list of str, optional) – The names of the features X

• output_names (list of str, optional) – The names of the outputs

• treatment_names (list of str, optional) – The names of the treatments

Returns

output – The output dataframe includes point estimate, standard error, z score, p value and confidence intervals of the estimated metric of each treatment on each outcome for each sample X[i]

Return type

DataFrame

translate(offset)

Update the results in place by translating by an offset.

Parameters

offset (array_like) – The offset by which to translate these results

zstat(value=0)

Get the z statistic of the metric of each treatment on each outcome for each sample X[i].

Parameters

value (float, default 0) – The mean value of the metric you’d like to test under null hypothesis.

Returns

zstat – The z statistic of the metric of each treatment on each outcome for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

array_like, shape (m, d_y, d_t) or (m, d_y)

property point_estimate

Get the point estimate of each treatment on each outcome for each sample X[i].

Returns

prediction – The point estimate of each treatment on each outcome for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

array_like, shape (m, d_y, d_t) or (m, d_y)

property stderr

Get the standard error of the metric of each treatment on each outcome for each sample X[i].

Returns

stderr – The standard error of the metric of each treatment on each outcome for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

array_like, shape (m, d_y, d_t) or (m, d_y)

property var

Get the variance of the metric of each treatment on each outcome for each sample X[i].

Returns

var – The variance of the metric of each treatment on each outcome for each sample X[i]. Note that when Y or T is a vector rather than a 2-dimensional array, the corresponding singleton dimensions in the output will be collapsed (e.g. if both are vectors, then the output of this method will also be a vector)

Return type

array_like, shape (m, d_y, d_t) or (m, d_y)