使用Python匹配Stata加权xtile命令的明确方法？

Question

对于项目,我需要复制当前存在于Stata输出文件(.dta)中的一些结果,并且是从较旧的Stata脚本计算的.该项目的新版本需要用Python编写.

我遇到困难的具体部分是基于Stata xtile命令的加权版本匹配分位数断点计算.请注意,数据点之间的关系与权重无关,而我使用的权重来自连续数量,因此关系极不可能(并且我的测试数据集中没有关系).所以由于关系而错误分类不是这样.

我已经阅读了关于加权百分位数的维基百科文章以及这个交叉验证的帖子,该文章描述了应该复制R的7型分位数的替代算法.

我已经实现了两种加权算法(底部的代码),但是我仍然不能很好地匹配Stata输出中的计算分位数.

有谁知道Stata例程使用的具体算法？文档没有清楚地描述这一点.它说的是在CDF的平坦部分采取平均值来反转它,但这几乎不能描述实际的算法,并且对于它是否正在进行任何其他插值是模棱两可的.

注意numpy.percentile并且scipy.stats.mstats.mquantiles不接受权重并且不能执行加权分位数,只是常规的等权重分数.我的问题的关键在于需要使用重量.

注意:我已经在下面调试了两种方法,但如果你看到一个,可以随意在评论中提出错误.我已经在较小的数据集上测试了这两种方法,结果很好,并且在我可以保证R使用的方法的情况下也匹配R的输出.代码不是那么优雅,而且在两种类型之间复制的太多,但是当我相信输出是我需要的时候,所有这些都将被修复.

问题是我不知道Stata xtile使用的方法,并且我希望减少下面的代码和Stata xtile在同一数据集上运行时的不匹配.

我试过的算法:

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

Answer 1

以下是 Stata 12 手册中的公式屏幕截图（StataCorp.2011。Stata 统计软件：第 12 版。德克萨斯州大学城：StataCorp LP，第 501-502 页）。如果这没有帮助，您可以在 Statalist 上问这个问题或直接联系 Philip Ryan（原始代码的作者）。