对于一个项目，我需要复制 Stata 输出文件 (.dta) 中当前存在的一些结果，这些结果是根据较旧的 Stata 脚本计算得出的。新版本的项目需要用Python编写。
我遇到困难的具体部分是根据 Stata 的加权版本匹配分位数断点计算xtile command。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，由于关系而错误分类并非如此。
我已阅读维基百科关于加权百分位数的文章并且这个交叉验证的帖子描述了一种应该复制 R 的 7 类分位数的替代算法。
我已经实现了两种加权算法（代码在底部），但我仍然没有很好地匹配 Stata 输出中计算的分位数。
有谁知道Stata例程使用的具体算法吗？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，但这几乎无法描述实际的算法，并且对于它是否正在执行任何其他插值也含糊不清。
注意numpy.percentile and scipy.stats.mstats.mquantiles不接受权重，也不能执行加权分位数，仅执行常规等权分位数。我的问题的关键在于需要使用权重。
注意：我已经对下面的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。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与 R 的输出相匹配。该代码还不是那么优雅，并且在两种类型之间复制了太多内容，但是当我相信输出是我需要的时，所有这些都将在稍后修复。
问题是我不知道Stata的方法xtile使用，我想减少下面的代码和 Stata 之间的不匹配xtile当在相同的数据集上运行时。
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
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）。
