Module stikpetP.other.poho_residual_gof_gof

Functions

def ph_residual_gof_gof(data, test='pearson', expCount=None, mtc='bonferroni', **kwargs)

Post-Hoc Residuals Using GoF for GoF

This function will perform a goodness-of-fit test using each category and collapsing the other categories.

The unadjusted p-values and Bonferroni adjusted p-values are both determined.

This function is shown in this YouTube video and the test is also described at PeterStatistics.com

Parameters

data : list or pandas series

 

test : {"pearson", "freeman-tukey", "freeman-tukey-read", "g", "mod-log-g", "neyman", "powerdivergence", "multinomial"}, optional

test to use

expCount : pandas dataframe, optional

categories and expected counts

mtc : string, optional

any of the methods available in p_adjust() to correct for multiple tests

**kwargs : optional

additional arguments for the specific test that are passed along.

Returns

pandas.DataFrame

A dataframe with the following columns:

• category, the label of the category
• obs. count, the observed count
• exp. count, the expected count
• statistic, the chi-square test statistic
• df, the degrees of freedom or in case
• p-value, the unadjusted significance
• adj. p-value, the adjusted significance
• minExp, the minimum expected count
• percBelow5, the percentage of cells with an expected count below 5

• test, description of the test used

• In case of a multinomial test, the same columns except

• p obs instead of statistic, showing the probability of the observed sample table
• n combs., instead of df, showing the number of possible tables
• no minExp and propBelow5 column.

Notes

none.

Before, After and Alternatives

Before this an omnibus test might be helpful, these are also the tests used on each category: * ts_pearson_gof for Pearson Chi-Square Goodness-of-Fit Test * ts_freeman_tukey_gof for Freeman-Tukey Test of Goodness-of-Fit * ts_freeman_tukey_read for Freeman-Tukey-Read Test of Goodness-of-Fit * ts_g_gof for G (Likelihood Ratio) Goodness-of-Fit Test * ts_mod_log_likelihood_gof for Mod-Log Likelihood Test of Goodness-of-Fit * ts_multinomial_gof for Multinomial Goodness-of-Fit Test * ts_neyman_gof for Neyman Test of Goodness-of-Fit * ts_powerdivergence_gof for Power Divergence GoF Test

After this you might want to add an effect size measure: * es_post_hoc_gof for various effect sizes

Alternative post-hoc tests: * ph_pairwise_bin for Pairwise Binary Test * ph_pairwise_gof for Pairwise Goodness-of-Fit Tests * ph_residual_gof_bin for Residuals Tests

More info on the adjustment for multiple testing: * p_adjust

Author

Made by P. Stikker

Companion website: https://PeterStatistics.com
YouTube channel: https://www.youtube.com/stikpet
Donations: https://www.patreon.com/bePatron?u=19398076

Examples

Examples: get data

>>> import pandas as pd
>>> pd.set_option('display.width',1000)
>>> pd.set_option('display.max_columns', 1000)    
>>> gss_df = pd.read_csv('https://peterstatistics.com/Packages/ExampleData/GSS2012a.csv', sep=',', low_memory=False, storage_options={'User-Agent': 'Mozilla/5.0'})
>>> ex1 = gss_df['mar1'];

Example 1 using default settings:

>>> ph_residual_gof_gof(ex1)
        category  obs. count  exp. count    statistic   df        p-value   adj. p-value  minExp  percBelow5                                   test used
0        MARRIED       972.0       388.2  1097.444745  1.0  1.186466e-240  5.932332e-240   388.2         0.0  Pearson chi-square test of goodness-of-fit
1  NEVER MARRIED       395.0       388.2     0.148892  1.0   6.995961e-01   1.000000e+00   388.2         0.0  Pearson chi-square test of goodness-of-fit
2       DIVORCED       314.0       388.2    17.728104  1.0   2.548337e-05   1.274169e-04   388.2         0.0  Pearson chi-square test of goodness-of-fit
3        WIDOWED       181.0       388.2   138.240082  1.0   6.457789e-32   3.228895e-31   388.2         0.0  Pearson chi-square test of goodness-of-fit
4      SEPARATED        79.0       388.2   307.845956  1.0   6.433895e-69   3.216947e-68   388.2         0.0  Pearson chi-square test of goodness-of-fit

Example 2 using a G test and Holm correction:

>>> ph_residual_gof_gof(ex1, test="g", mtc='holm')
        category  obs. count  exp. count   statistic   df        p-value   adj. p-value  minExp  percBelow5                  test used
0        MARRIED       972.0       388.2  870.406786  1.0  2.661640e-191  1.330820e-190   388.2         0.0  G test of goodness-of-fit
1  NEVER MARRIED       395.0       388.2    0.148246  1.0   7.002168e-01   7.002168e-01   388.2         0.0  G test of goodness-of-fit
2       DIVORCED       314.0       388.2   18.674271  1.0   1.550608e-05   3.101215e-05   388.2         0.0  G test of goodness-of-fit
3        WIDOWED       181.0       388.2  164.679720  1.0   1.074669e-37   3.224007e-37   388.2         0.0  G test of goodness-of-fit
4      SEPARATED        79.0       388.2  424.698965  1.0   2.315657e-94   9.262630e-94   388.2         0.0  G test of goodness-of-fit

Expand source code

def ph_residual_gof_gof(data, test="pearson", expCount=None, mtc='bonferroni', **kwargs):
    '''
    Post-Hoc Residuals Using GoF for GoF
    ----------------------------------------
    
    This function will perform a goodness-of-fit test using each category and collapsing the other categories.

    The unadjusted p-values and Bonferroni adjusted p-values are both determined.

    This function is shown in this [YouTube video](https://youtu.be/PF4Iuh0BDtQ) and the test is also described at [PeterStatistics.com](https://peterstatistics.com/Terms/Tests/PostHocAfterGoF.html)
    
    Parameters
    ----------
    data : list or pandas series
    test : {"pearson", "freeman-tukey", "freeman-tukey-read", "g", "mod-log-g", "neyman", "powerdivergence", "multinomial"}, optional 
        test to use
    expCount : pandas dataframe, optional 
        categories and expected counts
    mtc : string, optional
        any of the methods available in p_adjust() to correct for multiple tests
    **kwargs : optional
        additional arguments for the specific test that are passed along.
    
    Returns
    -------
    pandas.DataFrame
        A dataframe with the following columns:
    
        - *category*, the label of the category
        - *obs. count*, the observed count
        - *exp. count*, the expected count
        - *statistic*, the chi-square test statistic
        - *df*, the degrees of freedom or in case
        - *p-value*, the unadjusted significance
        - *adj. p-value*, the adjusted significance
        - *minExp*, the minimum expected count
        - *percBelow5*, the percentage of cells with an expected count below 5
        - *test*, description of the test used
        
        - In case of a multinomial test, the same columns except
        - *p obs* instead of *statistic*, showing the probability of the observed sample table
        - *n combs.*, instead of *df*, showing the number of possible tables
        - no *minExp* and *propBelow5* column.

    Notes
    -----
    none.
    
    Before, After and Alternatives
    ------------------------------
    Before this an omnibus test might be helpful, these are also the tests used on each category:
    * [ts_pearson_gof](../tests/test_pearson_gof.html#ts_pearson_gof) for Pearson Chi-Square Goodness-of-Fit Test
    * [ts_freeman_tukey_gof](../tests/test_freeman_tukey_gof.html#ts_freeman_tukey_gof) for Freeman-Tukey Test of Goodness-of-Fit
    * [ts_freeman_tukey_read](../tests/test_freeman_tukey_read.html#ts_freeman_tukey_read) for Freeman-Tukey-Read Test of Goodness-of-Fit
    * [ts_g_gof](../tests/test_g_gof.html#ts_g_gof) for G (Likelihood Ratio) Goodness-of-Fit Test
    * [ts_mod_log_likelihood_gof](../tests/test_mod_log_likelihood_gof.html#ts_mod_log_likelihood_gof) for Mod-Log Likelihood Test of Goodness-of-Fit
    * [ts_multinomial_gof](../tests/test_multinomial_gof.html#ts_multinomial_gof) for Multinomial Goodness-of-Fit Test
    * [ts_neyman_gof](../tests/test_neyman_gof.html#ts_neyman_gof) for Neyman Test of Goodness-of-Fit
    * [ts_powerdivergence_gof](../tests/test_powerdivergence_gof.html#ts_powerdivergence_gof) for Power Divergence GoF Test
    
    After this you might want to add an effect size measure:
    * [es_post_hoc_gof](../effect_sizes/eff_size_post_hoc_gof.html#es_post_hoc_gof) for various effect sizes
    
    Alternative post-hoc tests:
    * [ph_pairwise_bin](../other/poho_pairwise_bin.html#ph_pairwise_bin) for Pairwise Binary Test
    * [ph_pairwise_gof](../other/poho_pairwise_gof.html#ph_pairwise_gof) for Pairwise Goodness-of-Fit Tests
    * [ph_residual_gof_bin](../other/poho_residual_gof_bin.html#ph_residual_gof_bin) for Residuals Tests
    
    More info on the adjustment for multiple testing:
    * [p_adjust](../other/p_adjustments.html#p_adjust)
    
    Author
    ------
    Made by P. Stikker
    
    Companion website: https://PeterStatistics.com  
    YouTube channel: https://www.youtube.com/stikpet  
    Donations: https://www.patreon.com/bePatron?u=19398076

    Examples
    --------
    Examples: get data
    >>> import pandas as pd
    >>> pd.set_option('display.width',1000)
    >>> pd.set_option('display.max_columns', 1000)    
    >>> gss_df = pd.read_csv('https://peterstatistics.com/Packages/ExampleData/GSS2012a.csv', sep=',', low_memory=False, storage_options={'User-Agent': 'Mozilla/5.0'})
    >>> ex1 = gss_df['mar1'];

    Example 1 using default settings:
    >>> ph_residual_gof_gof(ex1)
            category  obs. count  exp. count    statistic   df        p-value   adj. p-value  minExp  percBelow5                                   test used
    0        MARRIED       972.0       388.2  1097.444745  1.0  1.186466e-240  5.932332e-240   388.2         0.0  Pearson chi-square test of goodness-of-fit
    1  NEVER MARRIED       395.0       388.2     0.148892  1.0   6.995961e-01   1.000000e+00   388.2         0.0  Pearson chi-square test of goodness-of-fit
    2       DIVORCED       314.0       388.2    17.728104  1.0   2.548337e-05   1.274169e-04   388.2         0.0  Pearson chi-square test of goodness-of-fit
    3        WIDOWED       181.0       388.2   138.240082  1.0   6.457789e-32   3.228895e-31   388.2         0.0  Pearson chi-square test of goodness-of-fit
    4      SEPARATED        79.0       388.2   307.845956  1.0   6.433895e-69   3.216947e-68   388.2         0.0  Pearson chi-square test of goodness-of-fit

    Example 2 using a G test and Holm correction:
    >>> ph_residual_gof_gof(ex1, test="g", mtc='holm')
            category  obs. count  exp. count   statistic   df        p-value   adj. p-value  minExp  percBelow5                  test used
    0        MARRIED       972.0       388.2  870.406786  1.0  2.661640e-191  1.330820e-190   388.2         0.0  G test of goodness-of-fit
    1  NEVER MARRIED       395.0       388.2    0.148246  1.0   7.002168e-01   7.002168e-01   388.2         0.0  G test of goodness-of-fit
    2       DIVORCED       314.0       388.2   18.674271  1.0   1.550608e-05   3.101215e-05   388.2         0.0  G test of goodness-of-fit
    3        WIDOWED       181.0       388.2  164.679720  1.0   1.074669e-37   3.224007e-37   388.2         0.0  G test of goodness-of-fit
    4      SEPARATED        79.0       388.2  424.698965  1.0   2.315657e-94   9.262630e-94   388.2         0.0  G test of goodness-of-fit
    
    '''
    if type(data) is list:
        data = pd.Series(data)
            
    freq = data.value_counts()
        
    if expCount is None:
        #assume all to be equal
        n = sum(freq)
        k = len(freq)
        categories = list(freq.index)
        expC = [n/k] * k
        
    else:
        #check if categories match
        nE = 0
        n = 0
        for i in range(0, len(expCount)):
            nE = nE + expCount.iloc[i,1]
            n = n + freq[expCount.iloc[i,0]]
        
        expC = []
        for i in range(0,len(expCount)):
            expC.append(expCount.iloc[i, 1]/nE*n)
            
        k = len(expC)
        categories = list(expCount.iloc[:,0])
    
    results = pd.DataFrame()
    resRow=0
    for i in range(0, k):
        cat = categories[i]
        results.at[resRow, 0] = cat
        
        n1 = freq[categories[i]]
        results.at[resRow, 1] = n1
        
        e1 = expC[i]
        results.at[resRow, 2] = e1
        tempA = [categories[i]]*n1
        tempB = ['all other']*(n - n1)
        temp_data = tempA + tempB
        exP = pd.DataFrame([[categories[i], e1], ['all other', n - e1]], columns=['category', 'count'])
        if test=="pearson":                
            pair_test_result = ts_pearson_gof(temp_data, expCounts=exP, **kwargs)
        elif test=="freeman-tukey":
            pair_test_result = ts_freeman_tukey_gof(temp_data, expCounts=exP, **kwargs)
        elif test=="freeman-tukey-read":
            pair_test_result = ts_freeman_tukey_read(temp_data, expCounts=exP, **kwargs)
        elif test=="g":
            pair_test_result = ts_g_gof(temp_data, expCounts=exP, **kwargs)
        elif test=="mod-log-g":
            pair_test_result = ts_mod_log_likelihood_gof(temp_data, expCounts=exP, **kwargs)
        elif test=="neyman":
            pair_test_result = ts_neyman_gof(temp_data, expCounts=exP, **kwargs)
        elif test=="powerdivergence":
            pair_test_result = ts_powerdivergence_gof(temp_data, expCounts=exP, **kwargs)

        if test=="multinomial":
            pair_test_result = ts_multinomial_gof(temp_data, expCounts=exP, **kwargs)
            results.at[resRow, 3] = pair_test_result.iloc[0, 0]
            results.at[resRow, 4] = pair_test_result.iloc[0, 1]
            results.at[resRow, 5] = pair_test_result.iloc[0, 2]
            results.at[resRow, 6] = results.at[resRow, 5]
            results.at[resRow, 7] = pair_test_result.iloc[0, 3]
            
        else:
            results.at[resRow, 3] = pair_test_result.iloc[0, 2]
            results.at[resRow, 4] = pair_test_result.iloc[0, 3]
            results.at[resRow, 5] = pair_test_result.iloc[0, 4]
            results.at[resRow, 6] = results.at[resRow, 5]
            results.at[resRow, 7] = pair_test_result.iloc[0, 5]
            results.at[resRow, 8] = pair_test_result.iloc[0, 6]
            results.at[resRow, 9] = pair_test_result.iloc[0, 7]
          
        resRow = resRow + 1

    results.iloc[:,6] = p_adjust(results.iloc[:,6], method=mtc)
    
    if test == "multinomial":
        # Set columns for multinomial case
        results.columns = [
            "category", "obs. count", "exp. count", "p obs", "n combs.",
            "p-value", "adj. p-value", "test used"
        ]
    else:
        # Set columns for other cases
        results.columns = [
            "category", "obs. count", "exp. count", "statistic", "df", 
            "p-value", "adj. p-value", "minExp", "percBelow5", "test used"
        ]
    
    return results