使用Python匹配Stata加权xtil命令的确定方法？ [英] Definitive way to match Stata weighted xtile command using Python?

问题描述

对于一个项目，我需要复制一些结果，这些结果当前存在于Stata输出文件(.dta)中，并且是从较旧的Stata脚本计算得出的。项目的新版本需要用Python语言编写。

我遇到困难的具体部分是匹配基于Stataxtile command加权版本的分位数断点计算。请注意，数据点之间的关联与权重无关，而我使用的权重来自连续的数量，因此关联是极不可能的(并且我的测试数据集中没有关联)。因此，由于联系而导致的分类错误并不是问题所在。

我已阅读Wikipedia article on weighted percentiles和this Cross-Validated post，其中介绍了应复制R的第7类分位数的替代算法。

我已经实现了这两个加权算法(底部的代码)，但我仍然不能很好地匹配Stata输出中计算的分位数。

有人知道Stata例程使用的特定算法吗？文件没有明确描述这一点。它说的是在CDF的平坦部分取平均值来倒置它，但这几乎不能描述实际的算法，并且不清楚它是否正在进行任何其他内插。

请注意，numpy.percentile和scipy.stats.mstats.mquantiles不接受权重，也不能执行加权分位数，只能执行常规的等权分位数。我的问题的症结在于需要使用权重。

注意：我已经对下面的两种方法进行了相当多的调试，但如果您看到一个错误，请在评论中提出错误建议。我已经在较小的数据集上测试了这两种方法，结果很好，而且在我可以保证R使用的是什么方法的情况下，也符合R的输出。代码还不是很优雅，在两个类型之间复制了太多内容，但当我相信输出是我所需要的时，所有这些都会在稍后得到修复。

问题是我不知道Stataxtile使用的方法，我希望减少下面的代码与在相同数据集上运行的Stataxtile之间的不匹配。

我尝试过的算法：

import numpy as np

def mark_weighted_percentiles(a, labels, weights, type):
# a is an input array of values.
# weights is an input array of weights, so weights[i] goes with a[i]
# labels are the names you want to give to the xtiles
# type refers to which weighted algorithm. 
#      1 for wikipedia, 2 for the stackexchange post.

# The code outputs an array the same shape as 'a', but with
# labels[i] inserted into spot j if a[j] falls in x-tile i.
# The number of xtiles requested is inferred from the length of 'labels'.


# First type, "vanilla" weights from Wikipedia article.
if type == 1:

    # Sort the values and apply the same sort to the weights.
    N = len(a)
    sort_indx = np.argsort(a)
    tmp_a = a[sort_indx].copy()
    tmp_weights = weights[sort_indx].copy()

    # 'labels' stores the name of the x-tiles the user wants,
    # and it is assumed to be linearly spaced between 0 and 1
    # so 5 labels implies quintiles, for example.
    num_categories = len(labels)
    breaks = np.linspace(0, 1, num_categories+1)

    # Compute the percentile values at each explicit data point in a.
    cu_weights = np.cumsum(tmp_weights)
    p_vals = (1.0/cu_weights[-1])*(cu_weights - 0.5*tmp_weights)

    # Set up the output array.
    ret = np.repeat(0, len(a))
    if(len(a)<num_categories):
        return ret

    # Set up the array for the values at the breakpoints.
    quantiles = []


    # Find the two indices that bracket the breakpoint percentiles.
    # then do interpolation on the two a_vals for those indices, using
    # interp-weights that involve the cumulative sum of weights.
    for brk in breaks:
        if brk <= p_vals[0]: 
            i_low = 0; i_high = 0;
        elif brk >= p_vals[-1]:
            i_low = N-1; i_high = N-1;
        else:
            for ii in range(N-1):
                if (p_vals[ii] <= brk) and (brk < p_vals[ii+1]):
                    i_low  = ii
                    i_high = ii + 1       

        if i_low == i_high:
            v = tmp_a[i_low]
        else:
            # If there are two brackets, then apply the formula as per Wikipedia.
            v = tmp_a[i_low] + ((brk-p_vals[i_low])/(p_vals[i_high]-p_vals[i_low]))*(tmp_a[i_high]-tmp_a[i_low])

        # Append the result.
        quantiles.append(v)

    # Now that the weighted breakpoints are set, just categorize
    # the elements of a with logical indexing.
    for i in range(0, len(quantiles)-1):
        lower = quantiles[i]
        upper = quantiles[i+1]
        ret[ np.logical_and(a>=lower, a<upper) ] = labels[i] 

    #make sure upper and lower indices are marked
    ret[a<=quantiles[0]] = labels[0]
    ret[a>=quantiles[-1]] = labels[-1]

    return ret

# The stats.stackexchange suggestion.
elif type == 2:

    N = len(a)
    sort_indx = np.argsort(a)
    tmp_a = a[sort_indx].copy()
    tmp_weights = weights[sort_indx].copy()


    num_categories = len(labels)
    breaks = np.linspace(0, 1, num_categories+1)

    cu_weights = np.cumsum(tmp_weights)

    # Formula from stats.stackexchange.com post.
    s_vals = [0.0];
    for ii in range(1,N):
        s_vals.append( ii*tmp_weights[ii] + (N-1)*cu_weights[ii-1])
    s_vals = np.asarray(s_vals)

    # Normalized s_vals for comapring with the breakpoint.
    norm_s_vals = (1.0/s_vals[-1])*s_vals 

    # Set up the output variable.
    ret = np.repeat(0, N)
    if(N < num_categories):
        return ret

    # Set up space for the values at the breakpoints.
    quantiles = []


    # Find the two indices that bracket the breakpoint percentiles.
    # then do interpolation on the two a_vals for those indices, using
    # interp-weights that involve the cumulative sum of weights.
    for brk in breaks:
        if brk <= norm_s_vals[0]: 
            i_low = 0; i_high = 0;
        elif brk >= norm_s_vals[-1]:
            i_low = N-1; i_high = N-1;
        else:
            for ii in range(N-1):
                if (norm_s_vals[ii] <= brk) and (brk < norm_s_vals[ii+1]):
                    i_low  = ii
                    i_high = ii + 1   

        if i_low == i_high:
            v = tmp_a[i_low]
        else:
            # Interpolate as in the type 1 method, but using the s_vals instead.
            v = tmp_a[i_low] + (( (brk*s_vals[-1])-s_vals[i_low])/(s_vals[i_high]-s_vals[i_low]))*(tmp_a[i_high]-tmp_a[i_low])
        quantiles.append(v)

    # Now that the weighted breakpoints are set, just categorize
    # the elements of a as usual. 
    for i in range(0, len(quantiles)-1):
        lower = quantiles[i]
        upper = quantiles[i+1]
        ret[ np.logical_and( a >= lower, a < upper ) ] = labels[i] 

    #make sure upper and lower indices are marked
    ret[a<=quantiles[0]] = labels[0]
    ret[a>=quantiles[-1]] = labels[-1]

    return ret

推荐答案

以下是STATA 12手册(STATA Corp.2011年。STATA统计软件：Release 12.College Station，TX：StataCorp LP，p.501-502)。如果这不起作用，您可以在Statist上问这个问题，或者直接联系Philip Ryan(原始代码的作者)。

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