beta_equivalence function

Description

This function takes two logistic regression models M_A, M_B, sensitivity level \delta_\beta and significance level \alpha. It checks whether the coefficient vectors are equivalent.

Usage

beta_equivalence(model_a, model_b, delta, alpha)

Arguments

Value

equivalence

are the coefficient vectors equivalent? (boolean)

test_statistic

Equivalence test statistic

critical value

a level-\alpha critical value

ncp

non-centrality parameter

p_value

P-value

brier_score function

Description

This function takes a observations vector y and matching predictions vector \pi. It returns the Brier score for the predictions. Unless specified otherwise, input containing NAs will result with an NA.

Usage

brier_score(y, pi, na.rm = FALSE)

Arguments

Value

The Brier score \frac{1}{N}\sum_{i=1}^{N}{(y_i-\pi_i)^2}

Examples

brier_score(rbinom(10,1,seq(0.1, 1, 0.1)), seq(0.1, 1, 0.1))

descriptive_equiv function

Description

This function takes two datasets X_A, X_B, regression formula, significance level \alpha and sensitivity level \delta_\beta (either vector or scalar). It builds a logistic regression model for each of the datasets and then checks whether the obtained coefficient vectors are equivalent, using the beta_equivalence function.

Usage

descriptive_equiv(data_a, data_b, formula, delta, alpha = 0.05)

Arguments

Value

equivalence

the beta_equivalence function output

model_a

logistic regression model M_A

model_b

logistic regression model M_B

individual_predictive_equiv function

Description

This function takes two logistic regression models M_A, M_B, test data, significance level \alpha and allowed flips ratio r. It checks whether the models produce equivalent log-odds for the given test set and returns various figures.

Usage

individual_predictive_equiv(model_a, model_b, test_data, r = 0.1, alpha = 0.05)

Arguments

Value

equivalence

Are models M_A,M_B producing equivalent log-odds for the given test data? (boolean)

test_statistic

The test statistic

critical_value

a level-\alpha critical value the test

xi_bar

Mean \xi value for the test

delta_theta

Calculated equivalence parameter

p_value

P-value

performance_equiv function

Description

This function takes two logistic regression models M_A, M_B, test data, significance level \alpha and acceptable score degradation \delta_B. It checks whether the models perform equivalently on the test set and returns various figures.

Usage

performance_equiv(
  model_a,
  model_b,
  test_data,
  dv_index,
  delta_B = 1.1,
  alpha = 0.05
)

Arguments

Value

equivalence

Are models M_A,M_B producing equivalent Brier scores for the given test data? (boolean)

brier_score_ac

M_A Brier score on the testing data

brier_score_bc

M_B Brier score on the testing data

diff_sd_l

SD of the lower Brier difference BS^A-\delta_B^2BS^B

diff_sd_u

SD of the upper Brier difference BS^A-\delta_B^{-2}BS^B

test_stat_l

t_L equivalence boundary for the test

test_stat_u

t_U equivalence boundary for the test

crit_val

a level-\alpha critical value for the test

delta_B

Calculated equivalence parameter

p_value_l

P-value for t_L

p_value_u

P-value for t_U

Student Performance Data Set

Description

Data from a student achievement in secondary education of two Portuguese schools. Full attribute description could be found in the source webpage.

Usage

ptg_stud_data

Format

An object of class data.frame with 649 rows and 31 columns.

Details

The data used is taken from the Student Performance Data. The original data consists of 30 covariates (13 binary, 11 ordinal, 4 categorical, 2 numerical) and a numerical output variable indicating the students final grade in Portuguese Language course.

The data was split by gender (F/M) n_f=383, n_m=266. The target variable G3 was converted to binary, final_fail which indicates the cases where G3 < 10.

Next, each sub-population was divided into training and testing data, using a 4:1 ratio.

Source

https://archive.ics.uci.edu/ml/datasets/student+performance

References

P. Cortez and A. Silva. Using Data Mining to Predict Secondary School Student Performance. In A. Brito and J. Teixeira Eds., Proceedings of 5th FUture BUsiness TEChnology Conference (FUBUTEC 2008) pp. 5-12, Porto, Portugal, April, 2008, EUROSIS, ISBN 978-9077381-39-7.

See Also

http://www3.dsi.uminho.pt/pcortez/student.pdf

Student Performance Data Set - female testing data

Description

Student Performance Data Set - female testing data

Usage

ptg_stud_f_test

Format

An object of class data.frame with 77 rows and 30 columns.

See Also

ptg_stud_data

Student Performance Data Set - female training data

Description

Student Performance Data Set - female training data

Usage

ptg_stud_f_train

Format

An object of class data.frame with 306 rows and 30 columns.

See Also

ptg_stud_data

Student Performance Data Set - male testing data

Description

Student Performance Data Set - male testing data

Usage

ptg_stud_m_test

Format

An object of class data.frame with 53 rows and 30 columns.

See Also

ptg_stud_data

Student Performance Data Set - male training data

Description

Student Performance Data Set - male training data

Usage

ptg_stud_m_train

Format

An object of class data.frame with 213 rows and 30 columns.

See Also

ptg_stud_data

Sigmoid function

Description

This function takes a number \theta and returns its respective sigmoid probability \frac{e^{theta}}{1+e^{theta}}. This is used in logistic regression to model P(y=1|x).

Usage

sigmoid(theta)

Arguments

Value

the sigmoid probability

Examples

sigmoid(0)