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我目前正在尝试建模营销多渠道归因。我遇到的所有文章和包都使用特殊的“开始”状态，并且使用此处给出的以下矩阵运算（[Python 中的马尔可夫链]）[1] 基于该开始状态计算移除效果。

def removal_effects(df, conversion_rate):
removal_effects_dict = {}
channels = [channel for channel in df.columns if channel not in ['Start',
                                                                 'Null',
                                                                 'Conversion']]
for channel in channels:
    removal_df = df.drop(channel, axis=1).drop(channel, axis=0)
    for column in removal_df.columns:
        row_sum = np.sum(list(removal_df.loc[column]))
        null_pct = float(1) - row_sum
        if null_pct != 0:
            removal_df.loc[column]['Null'] = null_pct
        removal_df.loc['Null']['Null'] = 1.0

    removal_to_conv = removal_df[
        ['Null', 'Conversion']].drop(['Null', 'Conversion'], axis=0)
    removal_to_non_conv = removal_df.drop(
        ['Null', 'Conversion'], axis=1).drop(['Null', 'Conversion'], axis=0)

    removal_inv_diff = np.linalg.inv(
        np.identity(
            len(removal_to_non_conv.columns)) - np.asarray(removal_to_non_conv))
    removal_dot_prod = np.dot(removal_inv_diff, np.asarray(removal_to_conv))
    removal_cvr = pd.DataFrame(removal_dot_prod,
                               index=removal_to_conv.index)[[1]].loc['Start'].values[0]
    removal_effect = 1 - removal_cvr / conversion_rate
    removal_effects_dict[channel] = removal_effect

return removal_effects_dict

我的问题主要分为两部分：

  1. 我们可以将第一次触摸视为每条路径的开始状态吗？
  2. 如果没有开始状态，我们如何计算移除效果（任何文档或公式的解释都会非常有帮助）

我的参考资料：

https://gist.github.com/MortenHegewald/fb1d8051cd818c25283cbcbc4b587e5c#file-removal_effects-py

www.analyzecore.com/2016/08/03/attribution-model-r-part-1/

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