对于一个项目，我需要复制当前存在于 Stata 输出文件 (.dta) 中的一些结果，这些结果是从较旧的 Stata 脚本中计算出来的。项目的新版本需要用 Python 编写。
我遇到困难的具体部分是根据 Stataxtile命令的加权版本匹配分位数断点计算。请注意，数据点之间的联系与权重无关，并且我使用的权重来自连续数量，因此联系极不可能（并且我的测试数据集中没有联系）。因此，不是因为联系而导致分类错误。
我已经阅读了关于加权百分位数的 Wikipedia 文章以及这篇交叉验证的文章，该文章描述了一种替代算法，该算法应该复制 R 的 type-7 分位数。
我已经实现了这两种加权算法（底部的代码），但我仍然不能很好地与 Stata 输出中的计算分位数匹配。
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 的平坦部分取平均值来反转它，但这几乎没有描述实际的算法，并且对于它是否在做任何其他插值也模棱两可。
请注意，numpy.percentile并且scipy.stats.mstats.mquantiles不接受权重，也不能执行加权分位数，只是常规的等权分位数。我的问题的症结在于需要使用权重。
注意：我已经对以下两种方法进行了很多调试，但是如果您看到一个错误，请随时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，并且在我可以保证 R 使用什么方法的情况下也匹配 R 的输出。代码还不是很优雅，两种类型之间复制了太多，但是当我相信输出是我需要的时，所有这些都会在以后修复。
问题是我不知道Stataxtile使用的方法，我想减少下面的代码和Stataxtile在同一数据集上运行时的不匹配。
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
