彩种报告 - II.Rmd

---
title: "<span style='color:Red'>阿里彩票</span>"
subtitle: "彩种报告 (第II部)"
author: "雷欧 <img src='文艺坊图库/dashencaicai2.jpg' height='14'>"
date: "`r lubridate::today('Asia/Tokyo')`"
output:
  html_document: 
    mathjax: https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
    number_sections: yes
    toc: yes
    toc_depth: 4
    toc_float:
      collapsed: yes
      smooth_scroll: yes
    code_folding: hide
    css: CSSBackgrounds.css
---

# 主题

<img src='文艺坊图库/商场如战场.png' width='560'>

[[**主题曲**]{style="color:blue"}](https://github.com/englianhu/report/discussions)

🚄东方快车，🚄一带一路。

<audio controls loop autoplay src="文艺坊歌曲库/東方快車合唱團 Oriental Express - 紅紅青春敲呀敲 《黑松沙士》廣告主題曲.mp3" controls></audio>

<br>

# 设定

## SCSS 设置

<style>
pre {
  overflow-x: auto;
}
pre code {
  word-wrap: normal;
  white-space: pre;
}
.table-hover > tbody > tr:hover { 
  background-color: #8D918D;
}
</style>

```{r load-sass, class.source='bg-success', class.output='bg-primary'}
# install.packages('remotes', dependencies = TRUE, INSTALL_opts = '--no-lock')
library('BBmisc', 'rmsfuns')
#remotes::install_github("rstudio/sass")
lib('sass')

## https://support.rstudio.com/hc/en-us/articles/200532197
## https://community.rstudio.com/t/r-does-not-display-korean-chinese/30889/3?u=englianhu
#Sys.setlocale("LC_CTYPE", "en_US.UTF-8")
#Sys.setlocale("LC_CTYPE", "zh_CN.UTF-8")
#Sys.setlocale(category = "LC_CTYPE", "Chinese (Simplified)_China.936")
#Sys.setlocale(locale = "Chinese")
#Sys.setlocale(locale = "Japanese")
#Sys.setlocale(locale = "English")

# rmarkdown::render('/home/englianhu/Documents/owner/ryo-cn.Rmd',  encoding = 'UTF-8')
#Sys.setlocale("LC_CTYPE", "UTF-8")
#Sys.setlocale(locale = "UTF-8")
#Sys.setlocale(category = "LC_ALL", locale = "chs")
#Sys.setlocale(category = "LC_ALL", locale = "UTF-8")
#Sys.setlocale(category = "LC_ALL", locale = "Chinese")
#Sys.setlocale(category = "LC_ALL", locale = "zh_CN.UTF-8")
Sys.setlocale("LC_ALL", "en_US.UTF-8")
```

```{scss set-scss, class.source='bg-success', class.output='bg-primary'}
/* https://stackoverflow.com/a/66029010/3806250 */
h1 { color: #002C54; }
h2 { color: #2F496E; }
h3 { color: #375E97; }
h4 { color: #556DAC; }
h5 { color: #92AAC7; }

/* ----------------------------------------------------------------- */
/* https://gist.github.com/himynameisdave/c7a7ed14500d29e58149#file-broken-gradient-animation-less */
.hover01 {
  /* color: #FFD64D; */
  background: linear-gradient(155deg, #EDAE01 0%, #FFEB94 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #EDAE01 20%, #FFEB94 80%);
    }
  }

.hover02 {
  color: #FFD64D;
  background: linear-gradient(155deg, #002C54 0%, #4CB5F5 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #002C54 20%, #4CB5F5 80%);
    }
  }

.hover03 {
  color: #FFD64D;
  background: linear-gradient(155deg, #A10115 0%, #FF3C5C 100%);
  transition: all 0.45s;
  &:hover{
    background: linear-gradient(155deg, #A10115 20%, #FF3C5C 80%);
    }
  }
```

```{r gb-opts, class.source='hover01', class.output='hover02'}
## Set the timezone but not change the datetime
Sys.setenv(TZ = 'Asia/Shanghai')

## Setting to omit all warnings
## https://stackoverflow.com/a/36846793/3806250
## Set width
## options(knitr.table.format = 'html') will set all kableExtra tables to be 'html', otherwise need to set the parameter on every single table.
options(warn = -1, width = 999, knitr.table.format = 'html')#, digits.secs = 6)

## https://stackoverflow.com/questions/39417003/long-vectors-not-supported-yet-abnor-in-rmd-but-not-in-r-script
## https://yihui.org/knitr/options
knitr::opts_chunk$set(
  class.source = 'hover01', class.output = 'hover02', class.error = 'hover03', 
  message = FALSE, warning = FALSE, error = TRUE, 
  autodep = TRUE, aniopts = 'loop', 
  progress = TRUE, verbose = TRUE, 
  cache = FALSE, cache.lazy = FALSE, result = 'asis')
```

<br><br>

## 设置

```{r libs, eval=FALSE}
## Setup Options, Loading Required Libraries and Preparing Environment
## Loading the packages and setting adjustment
source('函数/libs.R')
```

读取程序包

```{r load-pkgs}
## Setup Options, Loading Required Libraries and Preparing Environment
## 3210448065@qq.com
## leiou123

## 2849108450@qq.com
## leiou123
## https://rstudio.cloud/project/1198888

## Loading the package 'BBmisc'
if(suppressMessages(!require('BBmisc'))){
  install.packages('BBmisc', dependencies = TRUE, INSTALL_opts = '--no-lock')
  suppressMessages(library('BBmisc'))
}
if (suppressMessages(!require('rmsfuns'))) {
  install.packages('rmsfuns', dependencies = TRUE, INSTALL_opts = '--no-lock')
  suppressMessages(library('rmsfuns'))
}

if(!require('REmap')) devtools::install_github('lchiffon/REmap')

## Loading multiple packages at once
#pkgs <- c('readr', 'plyr', 'dplyr', 'magrittr', 'tidyverse', 'devtools', 'zoo', 'lubridate', 'stringr', 'rvest', 'markdown', 'googleVis', 'knitr', 'rmarkdown', 'htmltools', 'knitr', 'kableExtra', 'formattable', 'echarts4r', 'radarchart', 'MASS', 'htmlwidgets', 'maps', 'REmap', 'ggmap', 'vembedr')

pkgs <- c('plyr', 'dplyr', 'magrittr', 'stringr', 'knitr', 'kableExtra', 'lubridate', 'broom', 'purrr', 'readxl', 'tibble', 'DT')

suppressAll(lib(pkgs))
load_pkg(pkgs)
rm(pkgs)

## Set the googleVis options first to change the behaviour of plot.gvis, so that 
##  only the chart component of the HTML file is written into the output file.
op <- options(gvis.plot.tag = 'chart')

## <audio src='music/bigmoney.mp3' autoplay controls loop></audio>
```

```{r set-prefer}
conflict_prefer('filter', 'dplyr')
conflict_prefer('select', 'dplyr')
conflict_prefer('mutate', 'dplyr')
conflict_prefer('rename', 'dplyr')
```

<br><br>

# 简介

当初在推广部门，**宋祖：宋组长**给个样本数据，我就尝试使用线性模型和时间序列`arima`模型分析了进粉业绩，详情请参考[阿里彩票 - 分析样本数据](https://rpubs.com/englianhu/ali)^[基于数据观测值太少^[[binary.com Interview Question I (Extention)](https://rpubs.com/englianhu/binary-Q1E)尝试分别使用`3个月`、`6个月`、`12个月`、`18个月`和`24个月`的数据，结果`12个月`的数据最为精准。]，所以暂时没有预测。]。然后转到运维部门分析了[阿里彩票 - 彩种报告](https://rpubs.com/englianhu/ali_bet_type)，只是基本分析彩种，将数据视觉化；此商业分析进一步使用混合线性模型分析数据，预测彩种盈利。

<br>
<br>

# 数据

<br>

读取样本数据。

```{r, results = 'asis', warning = FALSE}
## 读取数据
fls <- suppressWarnings(list.files('文艺数据库/彩种'))
smp <- fls %>% 
  llply(., function(x) {
    dtt <- x %>% str_replace_all('.xls', '') %>% ymd
    smpp <- read_excel(paste0('文艺数据库/彩种/', x)) %>% 
      .[-nrow(.),]
    data.frame('日期' = dtt, smpp)
  }) %>% bind_rows %>% 
    as_tibble %>% 
    mutate('彩种名称' = factor(彩种名称), '盈率' = as.numeric(percent(盈率))) %>% 
    mutate_if(is.character, as.numeric)
rm(fls)

nm <- names(smp)
names(smp) <- c('Date', 'Type', 'Bettor', 'Turnover', 'Won', 'Cancelled', 'Rebates', 'Profit', 'Profit_rate')

## 转化为大数据
smp2 <- smp
#smp2 <- copy_to(sc, smp2)

# smp2 %>% 
#   as_tibble %>% 
#   kbl('html', caption = '每日投注人数', escape = F) %>% 
#   kable_styling(
#     bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
#   scroll_box(height = '400px')
```

```{r}
smp %>% glimpse
```

<span style='color:Orange'>*图表2.1：数据简介*</span>

<s>上图</s>[阿里彩票 - 彩种报告](https://rpubs.com/englianhu/ali_bet_type)显示从`r smp$Date %>% range %>% .[1]`到`r smp$Date %>% range %>% .[2]`的报表数据，一共有`r nrow(smp2)`个观测值。

<br>
<br>

# 统计模型

<br>

## 多元相互式模型

<br>

以下数据显示每日投注人数。

```{r, results = 'asis', warning = FALSE}
# smp2 %>%
#     spark_apply(
#         function(e) summary(lm(Profit ~ Turnover * Bettor * Won, e))$r.squared,
#         names = 'r.squared',
#         group_by = 'Type')

# 每日观测值
smp2 %>% 
    ddply(.(Date), nrow) %>% 
    as_tibble %>% dplyr::rename(n = V1) %>% 
  ## https://www.colorhexa.com/color-names
  mutate(n = color_tile('#007fff', 'white')(n)) %>% #azure
  kbl('html', caption = '每日投注人数', escape = F, align = 'c') %>% 
  kable_styling(
    bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  scroll_box(height = '400px')
```

<span style='color:Orange'>*图表3.1.1：每日观测值*</span>

<br>

我不晓得最优模型，先以完整数据观测值为标准，以下乃`多元相互式模型`^[[如何 Estimate linear models](https://d.cosx.org/d/419820-estimate-linear-models/7)中的[UNDERSTANDING 3-WAY INTERACTIONS BETWEEN CONTINUOUS VARIABLES](https://tomhouslay.com/2014/03/21/understanding-3-way-interactions-between-continuous-variables/#comment-63365)]。

$$
\begin{align*}
 Y& = \beta_{0} + \beta_{1}X_{1} + \beta_{2}X_{2} + \beta_{3}X_{1}X_{2}\\ 
 &= \beta_{0} + {\color{Red} \widetilde{\beta_{1}}}X_{1} + \beta_{2}X_{2}; 
 {\color{Red} \widetilde{\beta_{1}}} = \beta_{1} + \beta_{2}X_{2}\\
\end{align*}
$$
<span style='color:Orange'>*方程3.1.1：多元相互式模型*（[*在线LaTEX方程编辑器*](https://www.codecogs.com/latex/eqneditor.php)）</span>

```{r, results = 'asis', eval = FALSE, warning = FALSE}
# lm1 <- lm(Profit ~ Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2)

# m.aic.backward1 <- step(lm1, direction = 'backward', trace = 1)
# m.aic.backward2 <- step(lm1)

md <- list(
  m00 = lm(Profit ~ Date * Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m01 = lm(Profit ~ Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m02 = lm(Profit ~ Type * Bettor * Turnover * Won * Cancelled, smp2) %>% extractAIC, 
  m03 = lm(Profit ~ Type * Bettor * Turnover * Won * Rebates, smp2) %>% extractAIC, 
  m04 = lm(Profit ~ Type * Bettor * Turnover * Cancelled * Rebates, smp2) %>% extractAIC, 
  m05 = lm(Profit ~ Type * Bettor * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m06 = lm(Profit ~ Type * Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m07 = lm(Profit ~ Bettor * Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m08 = lm(Profit ~ Type * Bettor * Turnover * Won, smp2) %>% extractAIC, 
  m09 = lm(Profit ~ Type * Bettor * Turnover * Rebates, smp2) %>% extractAIC, 
  m10 = lm(Profit ~ Type * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m11 = lm(Profit ~ Type * Bettor * Turnover * Cancelled, smp2) %>% extractAIC, 
  m12 = lm(Profit ~ Type * Bettor * Won * Rebates, smp2) %>% extractAIC, 
  m13 = lm(Profit ~ Type * Bettor * Won * Cancelled, smp2) %>% extractAIC, 
  m14 = lm(Profit ~ Type * Turnover * Won * Rebates, smp2) %>% extractAIC, 
  m15 = lm(Profit ~ Type * Turnover * Cancelled * Rebates, smp2) %>% extractAIC, 
  m16 = lm(Profit ~ Type * Turnover * Won * Rebates, smp2) %>% extractAIC, 
  m17 = lm(Profit ~ Type * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m18 = lm(Profit ~ Bettor * Turnover * Won * Cancelled, smp2) %>% extractAIC, 
  m19 = lm(Profit ~ Bettor * Turnover * Won * Rebates, smp2) %>% extractAIC, 
  m20 = lm(Profit ~ Bettor * Turnover * Cancelled * Rebates, smp2) %>% extractAIC, 
  m21 = lm(Profit ~ Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC, 
  m22 = lm(Profit ~ Turnover * Won * Cancelled * Rebates, smp2) %>% extractAIC) %>% 
  ldply %>% 
  as_tibble %>% 
  dplyr::rename(df = V1, AIC = V2)

## save files, easier to read.
microbenchmark(
   save(md, file = '文艺数据库/md.rda'), 
   write_rds(md, '文艺数据库/md.rds'), 
   saveRDS(md, file = '文艺数据库/md.rds'))
#Unit: microseconds
#                                expr     min       lq     mean   median      uq     max neval
#      save(md, "文艺数据库/md.rda") 114.666 130.9080 135.2061 134.3990 137.111 174.759   100
# write_rds(md, "文艺数据库/md.rds") 111.098 120.6370 126.8601 125.1935 129.534 178.582   100
#   saveRDS(md, "文艺数据库/md.rds") 143.649 160.3135 178.6935 183.2730 186.673 358.803   100
```

1) $m00 = lm(Profit \sim Date * Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
2) $m01 = lm(Profit \sim Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
3) $m02 = lm(Profit \sim Type * Bettor * Turnover * Won * Cancelled, smp2)$
4) $m03 = lm(Profit \sim Type * Bettor * Turnover * Won * Rebates, smp2)$
5) $m04 = lm(Profit \sim Type * Bettor * Turnover * Cancelled * Rebates, smp2)$
6) $m05 = lm(Profit \sim Type * Bettor * Won * Cancelled * Rebates, smp2)$
7) $m06 = lm(Profit \sim Type * Turnover * Won * Cancelled * Rebates, smp2)$
8) $m07 = lm(Profit \sim Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
9) $m08 = lm(Profit \sim Type * Bettor * Turnover * Won, smp2)$
10) $m09 = lm(Profit \sim Type * Bettor * Turnover * Rebates, smp2)$
11) $m10 = lm(Profit \sim Type * Won * Cancelled * Rebates, smp2)$
12) $m11 = lm(Profit \sim Type * Bettor * Turnover * Cancelled, smp2)$
13) $m12 = lm(Profit \sim Type * Bettor * Won * Rebates, smp2)$
14) $m13 = lm(Profit \sim Type * Bettor * Won * Cancelled, smp2)$
15) $m14 = lm(Profit \sim Type * Turnover * Won * Rebates, smp2)$
16) $m15 = lm(Profit \sim Type * Turnover * Cancelled * Rebates, smp2)$
17) $m16 = lm(Profit \sim Type * Turnover * Won * Rebates, smp2)$
18) $m17 = lm(Profit \sim Type * Won * Cancelled * Rebates, smp2)$
19) $m18 = lm(Profit \sim Bettor * Turnover * Won * Cancelled, smp2)$
20) $m19 = lm(Profit \sim Bettor * Turnover * Won * Rebates, smp2)$
21) $m20 = lm(Profit \sim Bettor * Turnover * Cancelled * Rebates, smp2)$
22) $m21 = lm(Profit \sim Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
23) $m22 = lm(Profit \sim Turnover * Won * Cancelled * Rebates, smp2)$

<span style='color:Orange'>*方程3.1：多元相互式模型*</span>

以上模型使用$lm()$函数，从模型$m00 \sim m22$，[How to Make Beautiful Tables in R](https://rfortherestofus.com/2019/11/how-to-make-beautiful-tables-in-r/)有很多桌表程序包，以下咱们比较下**最优模型**。

<br>

### formattable

<br>

```{r, results = 'asis', warning = FALSE}
md <- read_rds('文艺数据库/md.rds')
md2 <- md

## https://www.colorhexa.com/color-names
md2 %>% 
  formattable(
    list(
        AIC = formatter('span', style = x ~ formattable::style(
            color = ifelse(rank(x) <= 3, 'darkgoldenrod', 'grey')), 
            x ~ paste0(round(x, 2), 
                       ' (rank: ', sprintf('%1.f', rank(x)), ')')))) %>% 
    mutate(df = color_tile('#2a52be', 'white')(df)) #colbalt
```

<span style='color:Orange'>*方程3.1.1：最优多元相互式模型AIC比较*</span>

<br>

### kableExtra

<br>

```{r, results = 'asis', warning = FALSE}
## https://www.colorhexa.com/color-names
md2 %>% 
  mutate(
    df = color_tile('#2a52be', 'white')(df), #colbalt
    AIC = ifelse(
      rank(AIC) <= 3, 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'darkgoldenrod', bold = T), 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'grey', italic = T))) %>% 
  kbl('html', caption = '最优模型', escape = F, align = c('c', 'r', 'r')) %>% 
  kable_styling(
    bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  kable_material() %>% 
  scroll_box(height = '400px')
```

<span style='color:Orange'>*方程3.1.2：最优多元相互式模型AIC比较*</span>

<br>

以下模型乃前三榜，分别是$m00$所有因素，包括时间序列参数因素；$m07$忽略彩种因素；$m22$只包括`投注金额`、`中奖金额`、`撤单金额`和`返点金额`因素。

1) $m00 = lm(Profit \sim Date * Type * Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
8) $m07 = lm(Profit \sim Bettor * Turnover * Won * Cancelled * Rebates, smp2)$
23) $m22 = lm(Profit \sim Turnover * Won * Cancelled * Rebates, smp2)$

<span style='color:Orange'>*方程3.2.1：多元相互式模型*</span>

<span style='color:Red'>**备注**：以上最优模型加入时间变量，不过之后章节的时间序列模型，也得个别分析**$m00$**和**$m07$**，因为已经把时间变量加入分析，再加上时间序列的话，不晓得是否变质呢？</span>

<br>
<br>

## 多元多项式模型

<br>

### 多元正交与原始多项式模型

<br>

#### 多元多项式基本模型

<br>

- [关于r：拟合由`leaps :: regsubsets`选择的多项式回归模型](https://www.codenong.com/51223897)有举例，还介绍了`leaps`程序包。
- [lm()中的poly(): raw和正交之間的差異](https://www.itdaan.com/tw/c0fe14f3fda89205497a506bf9e9c119)
- [R实现Polynomial regression](https://www.jianshu.com/p/8e6cc12d3036)
- [多项式回归（Polynomial regression）及线性检验](https://www.bioinfo-scrounger.com/archives/polynomial-regression)
- [How to interpret coefficients from a polynomial model fit?](https://stats.stackexchange.com/a/95952/68357)
- [poly() in lm(): difference between raw vs. orthogonal](https://stackoverflow.com/a/30000214/3806250)
- [Fitting Polynomial Regression in R](https://www.r-bloggers.com/2015/09/fitting-polynomial-regression-in-r)^[Section**How to fit a polynomial regression** in [Fitting Polynomial Regression in R](https://www.r-bloggers.com/2015/09/fitting-polynomial-regression-in-r) ]
- [Raw or orthogonal polynomial regression?](https://stats.stackexchange.com/questions/258307/raw-or-orthogonal-polynomial-regression)
- [Multivariate polynomials in R (`polynom` package)](https://cran.r-project.org/web/packages/multipol/vignettes/multipol.pdf)^[[Multivariate polynomials in R (`polynom` package)](https://cran.r-project.org/web/packages/multipol/vignettes/multipol.pdf)可供R使用者使用多元非线性模型]
- [Multivariate Polynomial Regression in R (Prediction)](https://stackoverflow.com/a/50261058/3806250)
- [Polynomial regression with multiple independent variables in R](https://stackoverflow.com/questions/45013550/polynomial-regression-with-multiple-independent-variables-in-r)

![<span style='color:Orange'>*图像3.2.1：多项式线型模型*</span> [*Fitting Polynomial Regression in R*](https://www.r-bloggers.com/2015/09/fitting-polynomial-regression-in-r)](文艺坊图库/How to fit a polynomial regression 2.png)

<span style='color:Red'>**备注**：[lm() breaks when using poly() with predictors set up as factors](https://stackoverflow.com/a/61410867/3806250)讲述`poly`无法分析多元`factor`而只能分析虚拟变量（0或1）。</span>

$$
Y = \beta_{0} + \beta_{1}X_{1} + \beta_{11}X^{2} + \beta_{111}X^{3}
$$

<span style='color:Orange'>*方程3.1.2：多元多项式线型模型*</span>

<br>

##### 多元多项相互式正交模型

<br>

```{r, results = 'asis', eval = FALSE, warning = FALSE}
## https://stackoverflow.com/a/24133767/3806250
num <- 2:5

mprf_list <- llply(num, function(i) {
    mprf = list(
        #p00 = lm(Profit ~ 
        #         poly(Date, degree = i, raw = FALSE) * 
        #         poly(Bettor, degree = i, raw = FALSE) * 
        #         poly(Turnover, degree = i, raw = FALSE) * 
        #         poly(Won, degree = i, raw = FALSE) * 
        #         poly(Cancelled, degree = i, raw = FALSE) * 
        #         poly(Rebates, degree = i, raw = FALSE), smp2) %>% extractAIC, 
        {p01 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p01'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p01, paste0('文艺数据库/mprf', i, '_p01.rds'))}, 
        {p02 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p02'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p02, paste0('文艺数据库/mprf', i, '_p02.rds'))}, 
        {p03 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p03'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p03, paste0('文艺数据库/mprf', i, '_p03.rds'))}, 
        {p04 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p04'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p04, paste0('文艺数据库/mprf', i, '_p04.rds'))}, 
        {p05 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p05'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p05, paste0('文艺数据库/mprf', i, '_p05.rds'))}, 
        {p06 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p06'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p06, paste0('文艺数据库/mprf', i, '_p06.rds'))}, 
        {p07 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p07'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p07, paste0('文艺数据库/mprf', i, '_p07.rds'))}, 
        {p08 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p08'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p08, paste0('文艺数据库/mprf', i, '_p08.rds'))}, 
        {p09 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p09'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p09, paste0('文艺数据库/mprf', i, '_p09.rds'))}, 
        {p10 = lm(Profit ~ 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p10'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p10, paste0('文艺数据库/mprf', i, '_p10.rds'))}, 
        {p11 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p11'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p11, paste0('文艺数据库/mprf', i, '_p11.rds'))}, 
        {p12 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p12'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p12, paste0('文艺数据库/mprf', i, '_p12.rds'))}, 
        {p13 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p13'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p13, paste0('文艺数据库/mprf', i, '_p13.rds'))}, 
        {p14 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p14'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p14, paste0('文艺数据库/mprf', i, '_p14.rds'))}, 
        {p15 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p15'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p15, paste0('文艺数据库/mprf', i, '_p15.rds'))}, 
        {p16 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p16'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p16, paste0('文艺数据库/mprf', i, '_p16.rds'))}, 
        {p17 = lm(Profit ~ 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p17'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p17, paste0('文艺数据库/mprf', i, '_p17.rds'))}, 
        {p18 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p18'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p18, paste0('文艺数据库/mprf', i, '_p18.rds'))}, 
        {p19 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p19'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p19, paste0('文艺数据库/mprf', i, '_p19.rds'))}, 
        {p20 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p20'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p20, paste0('文艺数据库/mprf', i, '_p20.rds'))}, 
        {p21 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = FALSE) * 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p21'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p21, paste0('文艺数据库/mprf', i, '_p21.rds'))}, 
        {p22 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = FALSE) * 
                     poly(Won, degree = i, raw = FALSE) * 
                     poly(Cancelled, degree = i, raw = FALSE) * 
                     poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprf_p22'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p22, paste0('文艺数据库/mprf', i, '_p22.rds'))}
    ) %>% 
        ldply %>% 
        as_tibble
    
    ## save files, easier to read.
    #write_rds(mprf, paste0('文艺数据库/mprf', i, '.rds'))
})
```

<br>

##### 多元多项相互式原始模型

<br>

```{r, results = 'asis', eval = FALSE, warning = FALSE}
## https://stackoverflow.com/a/24133767/3806250
num <- 2:5

mprt_list <- llply(num, function(i) {
    mprt = list(
        #p00 = lm(Profit ~ 
        #         poly(Date, degree = i, raw = TRUE) * 
        #         poly(Bettor, degree = i, raw = TRUE) * 
        #         poly(Turnover, degree = i, raw = TRUE) * 
        #         poly(Won, degree = i, raw = TRUE) * 
        #         poly(Cancelled, degree = i, raw = TRUE) * 
        #         poly(Rebates, degree = i, raw = TRUE), smp2) %>% extractAIC, 
        {p01 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p01'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p01, paste0('文艺数据库/mprt', i, '_p01.rds'))}, 
        {p02 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p02'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p02, paste0('文艺数据库/mprt', i, '_p02.rds'))}, 
        {p03 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p03'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p03, paste0('文艺数据库/mprt', i, '_p03.rds'))}, 
        {p04 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p04'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p04, paste0('文艺数据库/mprt', i, '_p04.rds'))}, 
        {p05 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p05'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p05, paste0('文艺数据库/mprt', i, '_p05.rds'))}, 
        {p06 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p06'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p06, paste0('文艺数据库/mprt', i, '_p06.rds'))}, 
        {p07 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p07'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p07, paste0('文艺数据库/mprt', i, '_p07.rds'))}, 
        {p08 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p08'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p08, paste0('文艺数据库/mprt', i, '_p08.rds'))}, 
        {p09 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p09'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p09, paste0('文艺数据库/mprt', i, '_p09.rds'))}, 
        {p10 = lm(Profit ~ 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p10'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p10, paste0('文艺数据库/mprt', i, '_p10.rds'))}, 
        {p11 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p11'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p11, paste0('文艺数据库/mprt', i, '_p11.rds'))}, 
        {p12 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p12'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p12, paste0('文艺数据库/mprt', i, '_p12.rds'))}, 
        {p13 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p13'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p13, paste0('文艺数据库/mprt', i, '_p13.rds'))}, 
        {p14 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p14'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p14, paste0('文艺数据库/mprt', i, '_p14.rds'))}, 
        {p15 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p15'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p15, paste0('文艺数据库/mprt', i, '_p15.rds'))}, 
        {p16 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p16'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p16, paste0('文艺数据库/mprt', i, '_p16.rds'))}, 
        {p17 = lm(Profit ~ 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p17'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p17, paste0('文艺数据库/mprt', i, '_p17.rds'))}, 
        {p18 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p18'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p18, paste0('文艺数据库/mprt', i, '_p18.rds'))}, 
        {p19 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p19'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p19, paste0('文艺数据库/mprt', i, '_p19.rds'))}, 
        {p20 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p20'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p20, paste0('文艺数据库/mprt', i, '_p20.rds'))}, 
        {p21 = lm(Profit ~ 
                     poly(Bettor, degree = i, raw = TRUE) * 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p21'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p21, paste0('文艺数据库/mprt', i, '_p21.rds'))}, 
        {p22 = lm(Profit ~ 
                     poly(Turnover, degree = i, raw = TRUE) * 
                     poly(Won, degree = i, raw = TRUE) * 
                     poly(Cancelled, degree = i, raw = TRUE) * 
                     poly(Rebates, degree = i, raw = TRUE), smp2) %>% 
          extractAIC %>% 
          as_tibble %>% 
          t %>% as_tibble %>% 
          dplyr::rename(df = V1, AIC = V2) %>% 
          mutate(.md = paste0('mprt_p22'), degree = i, raw = TRUE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p22, paste0('文艺数据库/mprt', i, '_p22.rds'))}
    ) %>% 
        ldply %>% 
        as_tibble
    
    ## save files, easier to read.
    #write_rds(mprt, paste0('文艺数据库/mprt', i, '.rds'))
})
```

<br>

#### 多元多项相互式程度最优化

以下文章聊及多元多项相互式线型模型程度最优化。

```
To get a third order polynomial in x (x^3), you can do

lm(y ~ x + I(x^2) + I(x^3))
or

lm(y ~ poly(x, 3, raw=TRUE))
You could fit a 10th order polynomial and get a near-perfect fit, but should you?

EDIT: poly(x, 3) is probably a better choice (see @hadley below).
```

*出处：*[*Fitting polynomial model to data in R*](https://stackoverflow.com/a/3822706/3806250)

```
But what I want to say is that a polynomial of more than 3-5 degree is never useful! The critical reason is the Runge's phenomenon. In terms of statistical terminology: a high-order polynomial always badly overfits data!. Don't naively think that because orthogonal polynomials are numerically more stable than raw polynomials, Runge's effect can be eliminated. No, a polynomial of degree k forms a vector space, so whatever basis you use for representation, they have the same span!
```

*出处：*[*High (or very high) order polynomial regression in R (or alternatives?)*](https://stackoverflow.com/a/39803843/3806250)

```
Deciding on a degree
In performing a polynomial regression we must decide on the degree of the polynomial to use. One way to do this is by using hypothesis tests. We now fit models ranging from linear to a degree-5 polynomial and seek to determine the simplest model which is sufficient to explain the relationship between wage and age.

We can do this using the anova() function, which performs an analysis of variance (ANOVA, using an F-test) in order to test the null hypothesis that a model  M1  is sufficient to explain the data against the alternative hypothesis that a more complex model  M2  is required. In order to use the anova() function,  M1  and  M2  must be nested models: the predictors in  M1  must be a subset of the predictors in  M2 . In this case, we fit five different models and sequentially compare the simpler model to the more complex model:

fit_1 = lm(wage~age, data = Wage)
fit_2 = lm(wage~poly(age,2), data = Wage)
fit_3 = lm(wage~poly(age,3), data = Wage)
fit_4 = lm(wage~poly(age,4), data = Wage)
fit_5 = lm(wage~poly(age,5), data = Wage)
print(anova(fit_1,fit_2,fit_3,fit_4,fit_5))
```
[*7.8.1 Polynomial Regression and Step Functions7.8.1 Polynomial Regression and Step Functions*](http://www.science.smith.edu/~jcrouser/SDS293/labs/lab12-r.html#Deciding-on-a-degree)

![<span style='color:Orange'>*图像3.2.2a：分层多项式线型模型*</span> [*High (or very high) order polynomial regression in R (or alternatives?)*](https://stackoverflow.com/a/39803843/3806250)](文艺坊图库/polynomials and orthogonal polymials.png)

![<span style='color:Orange'>*图像3.2.2b：分层多项式线型模型*</span> [*High (or very high) order polynomial regression in R (or alternatives?)*](https://stackoverflow.com/a/39803843/3806250)](文艺坊图库/polynomials and orthogonal polymials 2.png)

![<span style='color:Orange'>*图像3.2.2c：分层多项式线型模型*</span> [*High (or very high) order polynomial regression in R (or alternatives?)*](https://stackoverflow.com/a/39803843/3806250)](文艺坊图库/polynomials and orthogonal polymials 3.png)

![<span style='color:Orange'>*图像3.2.3a：拟合由`leaps :: regsubsets`选择的多项式回归模型*</span> [*关于r：拟合由`leaps :: regsubsets`选择的多项式回归模型*](https://www.codenong.com/51223897)](文艺坊图库/拟合由leaps regsubsets选择的多项式回归模型1.png)

![<span style='color:Orange'>*图像3.2.3b：拟合由`leaps :: regsubsets`选择的多项式回归模型*</span> [*关于r：拟合由`leaps :: regsubsets`选择的多项式回归模型*](https://www.codenong.com/51223897)](文艺坊图库/拟合由leaps regsubsets选择的多项式回归模型2.png)

```{r}
mdp <- dir('data', pattern = '^mp') %>% 
    ldply(., function(x) {
        read_rds(paste0('文艺数据库/', x))
    }) %>% 
    as_tibble
```

```{r}
mdp %>% 
  mutate(
    df = color_tile('#2a52be', 'white')(df), #colbalt
    AIC = ifelse(
      rank(AIC) <= 3, 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'darkgoldenrod', bold = T), 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'grey', italic = T))) %>% 
  kbl('html', caption = '分组最优模型', escape = F, align = c('c', 'r', 'r')) %>% 
  kable_styling(
    bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  kable_material() %>% 
  pack_rows('多项式回归 2', 1, 22, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式回归 3', 23, 44, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式回归 4', 45, 65, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式回归 5', 67, 88, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式正交回归 2', 89, 110, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式正交回归 3', 111, 132, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式正交回归 4', 133, 154, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式正交回归 5', 155, 176, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式原始回归 2', 177, 198, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式原始回归 3', 199, 220, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式原始回归 4', 221, 242, label_row_css = 'background-color: #666; color: #fff;') %>% 
  pack_rows('多项式原始回归 5', 243, 264, label_row_css = 'background-color: #666; color: #fff;') %>% 
  scroll_box(height = '400px')
```

<span style='color:Orange'>*图表3.2.1.1：分组最优模型*</span>

```{r}
mdp %>% 
  arrange(AIC) %>% 
  mutate(
    df = color_tile('#2a52be', 'white')(df), #colbalt
    AIC = ifelse(
      rank(AIC) <= 3, 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'darkgoldenrod', bold = T), 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'grey', italic = T))) %>% 
  kbl('html', caption = '最优模型排行榜', escape = F, align = c('c', 'r', 'r')) %>% 
  kable_styling(
    bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  kable_material() %>% 
  scroll_box(height = '400px')
```

<span style='color:Orange'>*图表3.2.1.2：最优模型排行榜*</span>

<span style='color:Red'>**备注：由于耗时，以上多元多项式模型并无将模型内的参数个别优化**`p22 = lm(Profit ~ poly(Turnover, degree = 2, raw = TRUE) * ` `poly(Won, degree = 3, raw = TRUE) * ` `poly(Cancelled, degree = 4, raw = TRUE) * ` `poly(Rebates, degree = 5, raw = TRUE), smp2)`</span>^[[binary.com 面试试题 I - GARCH模型中的ARIMA(p,d,q)参数最优化](https://rpubs.com/englianhu/binary-Q1FiGJRGARCH)虽然是单变量模型，不过会自动高效处理并筛选最优`arima(p,d,q)`参数]

<br>
<br>

## 多元内嵌模型

<br>

以下文献包含`多元相互式模型`、`多项式模型`、`多元内嵌模型`。

- [如何 Estimate linear models](https://d.cosx.org/d/419820-estimate-linear-models)和[`lm()`包中formula 表达方法的问题](https://d.cosx.org/d/157623-157623)^[多相互作用和内嵌线性模型]
- [R-Blog : Using R and lme/lmer to fit different two- and three-level longitudinal models](https://www.r-bloggers.com/2015/04/using-r-and-lmelmer-to-fit-different-two-and-three-level-longitudinal-models/)^[原稿:[Using R and lme/lmer to fit different two- and three-level longitudinal models](https://rpsychologist.com/r-guide-longitudinal-lme-lmer)多元内嵌线型模型]
- [Linear Regression and group by in R](https://stats.stackexchange.com/questions/31204/why-do-i-get-wildly-different-results-for-polyraw-t-vs-poly)
- [using lm(poly) to get formula coeff[duplicate]](https://stackoverflow.com/questions/17457884/using-lmpoly-to-get-formula-coeff)
- [Fitting polynomial model to data in R](https://stackoverflow.com/questions/3822535/fitting-polynomial-model-to-data-in-r)
- [R LME4 mixed models with nesting and nesting-interactions](https://stackoverflow.com/questions/62423505/r-lme4-mixed-models-with-nesting-and-nesting-interactions)
- [lmer poly() function on interactions](https://stackoverflow.com/questions/58943913/lmer-poly-function-on-interactions)^[内嵌多项式线型模型(Polynomial Regression)]

```{r, eval = FALSE}
dir('data', pattern = '^m.+rds$') %>% 
    ldply(., function(x) {
        read_rds(paste0('文艺数据库/', x))
    }) %>% arrange(AIC) %>% 
    dplyr::slice(1:5) %>% 
  mutate(
    df = color_tile('#2a52be', 'white')(df), #colbalt
    AIC = ifelse(
      rank(AIC) <= 3, 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'darkgoldenrod', bold = T), 
      cell_spec(
        paste0(round(AIC, 2), ' (rank: ', sprintf('%1.f', rank(AIC)), ')'), 
        'html', color = 'grey', italic = T))) %>% 
  kbl('html', caption = '最优模型', escape = F, align = c('c', 'r', 'r')) %>% 
  kable_styling(
    bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>% 
  kable_material() %>% 
  scroll_box(height = '400px')
```

由于多项式线型模型无法列入时间序列参数和因子参数，故此`lm(Profit ~ poly(Bettor, degree = i, raw = TRUE) * ` `poly(Turnover, degree = i, raw = TRUE) * ` `poly(Won, degree = i, raw = TRUE) * ` `poly(Cancelled, degree = i, raw = TRUE) * ` `poly(Rebates, degree = i, raw = TRUE), smp2)`为最优模型，这儿我先添加内嵌模型。

```{r, eval = FALSE}
mm = lmer(Profit ~ 
             poly(Bettor, degree = 2, raw = FALSE) * 
             poly(Turnover, degree = 2, raw = FALSE) * 
             poly(Won, degree = 2, raw = FALSE) * 
             poly(Cancelled, degree = 2, raw = FALSE) * 
             poly(Rebates, degree = 2, raw = FALSE) * (1/Date), smp2) %>% 
    extractAIC %>% 
    as_tibble %>% 
    t %>% as_tibble %>% 
    dplyr::rename(df = V1, AIC = V2) %>% 
    mutate(.md = paste0('mprf_p07'), degree = 2, raw = FALSE) %>% 
    dplyr::select(.md, degree, df, AIC)
write_rds(p07, paste0('文艺数据库/mprf', i, '_p07.rds'))



llply(5, function(i) {
    mprf = list(
        {mm01 = lm(Profit ~ Date * 
                       poly(Bettor, degree = i, raw = FALSE) * 
                       poly(Turnover, degree = i, raw = FALSE) * 
                       poly(Won, degree = i, raw = FALSE) * 
                       poly(Cancelled, degree = i, raw = FALSE) * 
                       poly(Rebates, degree = i, raw = FALSE), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p01'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(mm01, paste0('文艺数据库/mmprf', i, '_p01.rds'))}, 
        {mm02 = lmer(Profit ~ Date * 
                   poly(Bettor, degree = i, raw = FALSE) * 
                       poly(Turnover, degree = i, raw = FALSE) * 
                       poly(Won, degree = i, raw = FALSE) * 
                       poly(Cancelled, degree = i, raw = FALSE) * 
                     (1 / Date), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p02'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(mm02, paste0('文艺数据库/mmprf', i, '_p02.rds'))}, 
        {mm03 = lmer(Profit ~ Date * 
                      poly(Bettor, degree = i, raw = FALSE) * 
                      poly(Turnover, degree = i, raw = FALSE) * 
                      poly(Won, degree = i, raw = FALSE) * 
                      poly(Rebates, degree = i, raw = FALSE) * 
                     (1 / Type), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p03'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(mm03, paste0('文艺数据库/mmprf', i, '_p03.rds'))}, 
        {mm04 = lmer(Profit ~ Date * 
                      poly(Bettor, degree = i, raw = FALSE) * 
                      poly(Turnover, degree = i, raw = FALSE) * 
                      poly(Cancelled, degree = i, raw = FALSE) * 
                      poly(Rebates, degree = i, raw = FALSE) * 
                       (1 / Date) * (1 / Type), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p04'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p04, paste0('文艺数据库/mmprf', i, '_p04.rds'))}, 
        {mm05 = lmer(Profit ~ Date * 
                      poly(Bettor, degree = i, raw = FALSE) * 
                      poly(Won, degree = i, raw = FALSE) * 
                      poly(Cancelled, degree = i, raw = FALSE) * 
                      poly(Rebates, degree = i, raw = FALSE) * 
                     (Date / Type), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p05'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p05, paste0('文艺数据库/mmprf', i, '_p05.rds'))}, 
        {mm06 = lmer(Profit ~ Date * 
                      poly(Bettor, degree = i, raw = FALSE) * 
                      poly(Won, degree = i, raw = FALSE) * 
                      poly(Cancelled, degree = i, raw = FALSE) * 
                      poly(Rebates, degree = i, raw = FALSE) * 
                     (Type / Date), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p06'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p06, paste0('文艺数据库/mmprf', i, '_p06.rds'))}, 
        {mm07 = lmer(Profit ~ Date * 
                      poly(Bettor, degree = i, raw = FALSE) * 
                      poly(Won, degree = i, raw = FALSE) * 
                      poly(Cancelled, degree = i, raw = FALSE) * 
                      poly(Rebates, degree = i, raw = FALSE) * 
                     (1 + CondA * CondB | Sub) * (Type / Date), smp2) %>% 
            extractAIC %>% 
            as_tibble %>% 
            t %>% as_tibble %>% 
            dplyr::rename(df = V1, AIC = V2) %>% 
            mutate(.md = paste0('mmprf_p07'), degree = i, raw = FALSE) %>% 
            dplyr::select(.md, degree, df, AIC); 
        write_rds(p06, paste0('文艺数据库/mmprf', i, '_p07.rds'))}
    ) %>% 
        ldply %>% 
        as_tibble

## random effects with nested model
mm000 = lmer(Profit ~ Date * 
              poly(Bettor, degree = 2, raw = FALSE) * 
              poly(Won, degree = 2, raw = FALSE) * 
              poly(Cancelled, degree = 2, raw = FALSE) * 
              poly(Rebates, degree = 2, raw = FALSE) * 
              (1 + Won * Cancelled | Bettor) * (Type / Date), smp2) %>% 
    extractAIC
write_rds(mm000, paste0('文艺数据库/mm000.rds'))

## nested model
mm001 = lm(Profit ~ Date * 
               poly(Bettor, degree = 2, raw = FALSE) * 
               poly(Won, degree = 2, raw = FALSE) * 
               poly(Cancelled, degree = 2, raw = FALSE) * 
               poly(Rebates, degree = 2, raw = FALSE) * 
               (1 + Won * Cancelled / Bettor) * (Type / Date), smp2) %>% 
    extractAIC
write_rds(mm001, paste0('文艺数据库/mm001.rds'))

## lmer(y~poly(x,2,raw=TRUE)+(1|f)+(0+x|f)+(0+I(x^2)|f),
##            data=d)

## random effects with nested model
mm000_d3 = lmer(Profit ~ Date * 
              poly(Bettor, degree = 3, raw = FALSE) * 
              poly(Won, degree = 3, raw = FALSE) * 
              poly(Cancelled, degree = 3, raw = FALSE) * 
              poly(Rebates, degree = 3, raw = FALSE) * 
              (1 + Won * Cancelled | Bettor) * (Type / Date), smp2) %>% 
    extractAIC
write_rds(mm000_d3, paste0('文艺数据库/mm000_d3.rds'))

## nested model
mm001_d3 = lm(Profit ~ Date * 
               poly(Bettor, degree = 3, raw = FALSE) * 
               poly(Won, degree = 3, raw = FALSE) * 
               poly(Cancelled, degree = 3, raw = FALSE) * 
               poly(Rebates, degree = 3, raw = FALSE) * 
               (1 + Won * Cancelled / Bettor) * (Type / Date), smp2) %>% 
    extractAIC
write_rds(mm001_d3, paste0('文艺数据库/mm001_d4.rds'))

```

<br>
<br>

## 混合模型

<br>

以下文献包含`多元相互式模型`、`多项式模型`、`多元内嵌模型`。

- [混合线性模型的实现（更新20190607）](https://zhuanlan.zhihu.com/p/63092231)
- [Linear Regression and group by in R](https://stackoverflow.com/a/12064463/3806250)
- [Why do I get wildly different results for poly(raw=T) vs. poly()?](https://stats.stackexchange.com/a/31222/68357)

![[*Linear Regression and group by in R*](https://stackoverflow.com/a/12064463/3806250)](文艺坊图库/nested-polynomial-lm.png)

```{r}
## https://stackoverflow.com/a/24133767/3806250


```

<br>
<br>

## 时间序列模型

<br>

上个章节谈及最优三个模型，这儿咱们得先瞧瞧*图表3.1：每日观测值*每日观测值再决定数据多寡。

```{r}

```


<br>
<br>

### 30天数据

<br>

```{r}
##https://stackoverflow.com/questions/24133356/how-to-replicate-a-ddply-behavior-that-uses-a-custom-function-with-dplyr/24133767#24133767

```

<br>
<br>

### 40天数据

<br>

....

<br>
<br>

# 绘图

<br>

## 投注人数

<br>

## 投注金额

<br>

## 中奖金额

<br>

## 撤单金额

<br>

## 返点金额

<br>

## 盈利

<br>

## 盈率

<br>
<br>

# 结论

<br>

## 总结

${\color{Black} \circledR} {\color{DarkGreen} \gamma} {\color{Red} \sigma} \; {\color{Blue} \xi} {\color{Red} \eta} {\color{Blue} g}$^[[Latex Equation](https://www.codecogs.com/latex/eqneditor.php)] 🎏^[[Emoji list](https://gist.github.com/rxaviers/7360908)]

<br>


<br><br>

# 附录

## 文书明细

以下乃此文书的文件信息。

- 文集建立日：2022-05-31
- 文集最新更新日：`r today('Asia/Shanghai')`
- `r R.version.string`
- [**rmarkdown**](https://github.com/rstudio/rmarkdown) 程序包版本：`r packageVersion('rmarkdown')`
- 文集版本：0.2.1
- 文集作者：[®γσ, ξηg Lιαη Ημ](https://rpubs.com/englianhu/ryo-cn)
- 猫舍：[源代码](https://github.com/englianhu/report)
- 追加附属信息

```{r info}
#suppressMessages(require('formattable', quietly = TRUE))
#suppressMessages(require('knitr', quietly = TRUE))
#suppressMessages(require('kableExtra', quietly = TRUE))
#suppressMessages(require('magittr', quietly = TRUE))
#suppressMessages(require('devtools', quietly = TRUE))

sys1 <- session_info()$platform |> 
    unlist() |> 
    {\(.) data.frame(row.names = 1:length(.), 
                     Category = names(.), session_info = .)}()

sys2 <- data.frame(Sys.info()) |> 
    {\(.) data.frame(Category = row.names(.), Sys.info = .[,1])}()

#remarks, dim(sys1), dim(sys2)
if (nrow(sys1) == 11 && nrow(sys2) == 8) {
  sys2 <- sys2 |> 
    {\(.) rbind(., data.frame(
    Category = c('rmarkdown', 'rsconnect', 'Current time'), 
    Sys.info = c(as.character(getwd()), 
                 as.character(packageVersion('rsconnect')), 
                 paste(as.character(lubridate::now('Asia/Shanghai')), 'CST 🗺'))))}()
  
} else if (nrow(sys1) == 10 && nrow(sys2) == 8) {
  sys1 <- rbind(sys1, data.frame(Category = '', session_info = ''))
  
  sys2 <- sys2 |> 
    {\(.) rbind(., data.frame(
    Category = c('rmarkdown', 'rsconnect', 'Current time'), 
    Sys.info = c(as.character(getwd()), 
                 as.character(packageVersion('rsconnect')), 
                 paste(as.character(lubridate::now('Asia/Shanghai')), 'CST 🗺'))))}()
}

sys <- cbind(sys1, sys2) |> 
  {\(.) 
    kbl(., caption = 'Additional session information:')}() |> 
  {\(.) 
    kable_styling(., bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))}() |> 
  {\(.) 
    row_spec(., 0, background = 'DimGrey', color = 'yellow')}() |> 
  {\(.) 
    column_spec(., 1, background = 'CornflowerBlue', color = 'red')}() |> 
  {\(.) 
    column_spec(., 2, background = 'grey', color = 'black')}() |> 
  {\(.) 
    column_spec(., 3, background = 'CornflowerBlue', color = 'blue')}() |> 
  {\(.) 
    column_spec(., 4, background = 'grey', color = 'white')}() |> 
  {\(.) 
    row_spec(., 11, bold = TRUE, color = 'yellow', background = '#D7261E')}()

rm(sys1, sys2)
sys
```

## 参考文献

1) [Free themes for Bootstrap](https://bootswatch.com/3/)
2) [R packages for optimal stratified sampling: a review and compared evaluation](https://www.researchgate.net/publication/327791484_R_packages_for_optimal_stratified_sampling_a_review_and_compared_evaluation/comments)
3) [Use of models in SamplingStrata](https://cran.r-project.org/web/packages/SamplingStrata/vignettes/models.html)
4) [Example of Using a Banner Image with RMarkdown](https://rpubs.com/thaufas/555157)
5) [IN R MARKDOWN, How Can I add a background image (HTML output)?](https://stackoverflow.com/questions/60498668/in-r-markdown-how-can-i-add-a-background-image-html-output)
6) [CSS Background Image Size Tutorial – How to Code a Full Page Background Image](https://www.freecodecamp.org/news/css-full-page-background-image-tutorial)
7) [GitHub : Statistical Rethinking (2022 Edition)](https://github.com/englianhu/stat_rethinking_2022)
8) [GitHub : `rethinking` package](https://github.com/englianhu/rethinking) McElreath 2020. Statistical Rethinking, 2nd edition
9) [GitHub : Stan](https://github.com/stan-dev)
10) [GitHub : Repository for distributing (some) stan-dev R packages](https://github.com/stan-dev/r-packages)
11) [书栈网](https://www.bookstack.cn/user/englianhu)

---

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