基於變量的權重值

Question

我有一套基本上是問題答案的值，但是當我計算出答案時，我想通過給出答案權重來假裝我有更好的答案分佈。這裏是展示一個簡單的例子代碼：

from pprint import pprint 

q1 = [ 
    'blue', 
    'orange', 
    'red', 
] 

q2 = [ 
    'male', 
    'female', 
] 

q3 = [ 
    '18-25', 
    '26-30', 
    '31-40', 
    '41+' 
] 

data = [ 
    {'q1': 1, 'q2': 1, 'q3': 0}, # orange, female, 18-25 
    {'q1': 0, 'q2': 1, 'q3': 0}, # blue, female, 18-25 
    {'q1': 1, 'q2': 0, 'q3': 0}, # orange, male, 18-25 
    {'q1': 2, 'q2': 1, 'q3': 1}, # red, female, 26-30 
    {'q1': 2, 'q2': 1, 'q3': 1}, # red, female, 26-30 
    {'q1': 1, 'q2': 0, 'q3': 1}, # orange, male, 18-25 
] 

counts = { 
    'q1': {}, 
    'q2': {}, 
    'q3': {} 
} 

respondent_value = 1 

for respondent in data: 
    q1_val = q1[respondent['q1']] 
    q2_val = q2[respondent['q2']] 
    q3_val = q3[respondent['q3']] 

    if q1_val not in counts['q1']: 
     counts['q1'][q1_val] = 0 

    counts['q1'][q1_val] += respondent_value 

    if q2_val not in counts['q2']: 
     counts['q2'][q2_val] = 0 

    counts['q2'][q2_val] += 1 

    if q3_val not in counts['q3']: 
     counts['q3'][q3_val] = 0 

    counts['q3'][q3_val] += respondent_value 

pprint(counts) 

目前這將打印以下值：

{'q1': {'blue': 1, 'orange': 3, 'red': 2}, 
'q2': {'female': 4, 'male': 2}, 
'q3': {'18-25': 3, '26-30': 3}} 

我想，而不是假裝我有以下人口：

• 50％男性
• 50％女性
• 40％18-15
• 60％26-30

怎麼會自動生成給予我要代表這是什麼數據的權重？對於與人口統計不符的給定值，我將假設權重爲1.

我對使用熊貓/ numpy感興趣，如果他們有幫助，但會使用任何最適合的工具。

對於單值加權我可能會做這樣的（我需要多個變量）：

from pprint import pprint 

q1 = [ 
    'blue', 
    'orange', 
    'red', 
] 

q2 = [ 
    'male', 
    'female', 
] 

q3 = [ 
    '18-25', 
    '26-30', 
    '31-40', 
    '41+' 
] 

data = [ 
    {'q1': 1, 'q2': 1, 'q3': 0}, # orange, female, 18-25 
    {'q1': 0, 'q2': 1, 'q3': 0}, # blue, female, 18-25 
    {'q1': 1, 'q2': 0, 'q3': 0}, # orange, male, 18-25 
    {'q1': 2, 'q2': 1, 'q3': 1}, # red, female, 26-30 
    {'q1': 2, 'q2': 1, 'q3': 1}, # red, female, 26-30 
    {'q1': 1, 'q2': 0, 'q3': 1}, # orange, male, 18-25 
] 


def get_counts(male_weight, female_weight): 
    counts = { 
     'q1': {}, 
     'q2': {}, 
     'q3': {} 
    } 

    for respondent in data: 
     q1_val = q1[respondent['q1']] 
     q2_val = q2[respondent['q2']] 
     q3_val = q3[respondent['q3']] 

     if q2_val == 'female': 
      respondent_value = female_weight 
     else: 
      respondent_value = male_weight 

     if q1_val not in counts['q1']: 
      counts['q1'][q1_val] = 0 

     counts['q1'][q1_val] += respondent_value 

     if q2_val not in counts['q2']: 
      counts['q2'][q2_val] = 0 

     counts['q2'][q2_val] += respondent_value 

     if q3_val not in counts['q3']: 
      counts['q3'][q3_val] = 0 

     counts['q3'][q3_val] += respondent_value 

    return counts 

total_respondents = len(data) * 1.0 
counts = get_counts(1, 1) 
print("Starting counts") 
print("=================") 
pprint(counts) 
print("\n") 

female_pop = 50 
male_pop = 50 

sample_females = (counts['q2']['female']/total_respondents) * 100 
sample_males = (counts['q2']['male']/total_respondents) * 100 

female_weight = female_pop/sample_females 
male_weight = male_pop/sample_males 

weighted_counts = get_counts(male_weight, female_weight) 
print("Weighted Counts") 
print("===============") 
pprint(weighted_counts) 

Answer 1

如果我理解正確的話，你想要的顏色響應的分佈，但你想給更多體重對樣本中代表性不足的年齡和性別羣體。例如，如果女性的回答率是男性的兩倍，那麼您希望男性的回答重兩倍。如果這是正確的，這裏是大熊貓的做法：

In [70]: df = pd.DataFrame(dict(color=["orange","blue","orange","red","red","orange"],gender=["female","female","male","female","female","male"], age=["18-25", "18-25", "18-25", "26-30", "26-30", "18-25"])) 

In [71]: gender_dist = pd.Series([.5,.5], index=["female","male"]) 

In [72]: age_dist = pd.Series([.4,.6], index=["18-25","26-30"]) 

計算權重，您需要適用於實現自己的目標年齡/性別分佈：

In [73]: gender_weights = gender_dist/df.gender.groupby(df.gender).count() 

In [74]: age_weights = age_dist/df.age.groupby(df.age).count() 

In [75]: age_weights 
Out[75]: 
18-25 0.1 
26-30 0.3 
dtype: float64 

透視樣本數據來獲得數每種顏色的，按年齡和性別：

In [76]: df["value"] = 1 

In [77]: pivoted = pd.pivot_table(df, values="value", columns="color", index=["gender","age"], aggfunc="count", fill_value=0) 

In [78]: pivoted 
Out[78]: 
color   blue orange red 
gender age      
female 18-25  1  1 0 
     26-30  0  0 2 
male 18-25  0  2 0 

重新索引你的權重與樞軸表索引對齊：

In [79]: index=pd.MultiIndex.from_product([gender_weights.index, age_weights.index], names=["gender","age"]) 

In [80]: gender_weights = gender_weights.reindex(index, level=0) 

In [81]: age_weights = age_weights.reindex(index, level=1) 

In [82]: age_weights 
Out[82]: 
gender age 
female 18-25 0.1 
     26-30 0.3 
male 18-25 0.1 
     26-30 0.3 
dtype: float64 

乘以權重：

In [83]: weighted_counts = pivoted.mul(age_weights, axis=0).mul(gender_weights, axis=0) 

In [84]: weighted_counts 
Out[84]: 
color   blue orange red 
gender age       
female 18-25 0.0125 0.0125 0.000 
     26-30 0.0000 0.0000 0.075 
male 18-25 0.0000 0.0500 0.000 
     26-30  NaN  NaN NaN 

獲取加權分佈，那麼它正常化：

In [85]: dist = weighted.sum() 

In [86]: dist/dist.sum() 
Out[86]: 
color 
blue  0.083333 
orange 0.416667 
red  0.500000 
dtype: float64