Get Libraries and Raw Data

library(tidyverse)

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## ✔ tibble  2.0.1       ✔ dplyr   0.8.0.1
## ✔ tidyr   0.8.1       ✔ stringr 1.4.0  
## ✔ readr   1.1.1       ✔ forcats 0.3.0

## ── Conflicts ───────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()

library(stringr)
Nat0306 <- read_delim("~/Dropbox/RProjects/Fertility Study/Nat0306.txt","\t", escape_double = FALSE)

## Parsed with column specification:
## cols(
##   Notes = col_character(),
##   State = col_character(),
##   StateCode = col_character(),
##   Age = col_character(),
##   AgeCode = col_character(),
##   Year = col_integer(),
##   YearCode = col_integer(),
##   Births = col_integer(),
##   FPop = col_character(),
##   Rate = col_character()
## )

## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)

## Warning: 66 parsing failures.
## row # A tibble: 5 x 5 col     row col   expected   actual    file                                     expected   <int> <chr> <chr>      <chr>     <chr>                                    actual 1  1637 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… file 2  1638 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… row 3  1639 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… col 4  1640 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… expected 5  1641 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na…
## ... ................. ... ........................................................................... ........ ........................................................................... ...... ........................................................................... .... ........................................................................... ... ........................................................................... ... ........................................................................... ........ ...........................................................................
## See problems(...) for more details.

Nat0717 <- read_delim("~/Dropbox/RProjects/Fertility Study/Nat0717.txt","\t", escape_double = FALSE)

## Parsed with column specification:
## cols(
##   Notes = col_character(),
##   State = col_character(),
##   StateCode = col_character(),
##   Age = col_character(),
##   AgeCode = col_character(),
##   Year = col_integer(),
##   YearCode = col_integer(),
##   Births = col_integer(),
##   FPop = col_character(),
##   Rate = col_character()
## )

## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)

## Warning: 73 parsing failures.
## row # A tibble: 5 x 5 col     row col   expected   actual    file                                     expected   <int> <chr> <chr>      <chr>     <chr>                                    actual 1  4539 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… file 2  4540 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… row 3  4541 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… col 4  4542 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na… expected 5  4543 <NA>  10 columns 1 columns '~/Dropbox/RProjects/Fertility Study/Na…
## ... ................. ... ........................................................................... ........ ........................................................................... ...... ........................................................................... .... ........................................................................... ... ........................................................................... ... ........................................................................... ........ ...........................................................................
## See problems(...) for more details.

Parsing Errors ??

Look at the data.

Solution

Select the variables we want. Convert the character variable Rate to numeric and eliminate the rows where this variable is na. Then combine the two dataframes using rbind.

We could probably do the rbind first and save a few lines of typing. Per-preocesing the two separate files eliminates the possibility of problems because of differences between these two files, which came from different queries.

Nat0306 %>% 
  select(State,Year,Age,Rate) %>% 
  mutate(Rate = as.numeric(Rate)) %>% 
  filter(!is.na(Rate)) -> Nat0306

## Warning: NAs introduced by coercion

glimpse(Nat0306)

## Observations: 1,224
## Variables: 4
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "Al…
## $ Year  <int> 2003, 2004, 2005, 2006, 2003, 2004, 2005, 2006, 2003, 2004…
## $ Age   <chr> "15-19 years", "15-19 years", "15-19 years", "15-19 years"…
## $ Rate  <dbl> 51.40, 51.02, 48.06, 51.83, 113.67, 113.48, 116.90, 121.36…

Nat0717 %>% 
  select(State,Year,Age,Rate) %>% 
  mutate(Rate = as.numeric(Rate)) %>% 
  filter(!is.na(Rate)) -> Nat0717

## Warning: NAs introduced by coercion

glimpse(Nat0717)

## Observations: 3,366
## Variables: 4
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "Al…
## $ Year  <int> 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016…
## $ Age   <chr> "15-19 years", "15-19 years", "15-19 years", "15-19 years"…
## $ Rate  <dbl> 52.07, 50.53, 48.30, 43.63, 40.53, 39.15, 34.32, 32.02, 30…

both = rbind(Nat0306,Nat0717)
summary(both)

##     State                Year          Age                 Rate       
##  Length:4590        Min.   :2003   Length:4590        Min.   :  3.93  
##  Class :character   1st Qu.:2006   Class :character   1st Qu.: 29.38  
##  Mode  :character   Median :2010   Mode  :character   Median : 60.67  
##                     Mean   :2010                      Mean   : 65.21  
##                     3rd Qu.:2014                      3rd Qu.:102.11  
##                     Max.   :2017                      Max.   :184.05

Create the Total Fertility Rate (TFR)

Now create a new dataframe with one row for each combination of State and Year. Create the variable TFR.

both %>% 
  group_by(State,Year) %>% 
  summarize(TFR = 5*sum(Rate)/1000) %>% 
  ungroup() -> SYTFR
glimpse(SYTFR)

## Observations: 765
## Variables: 3
## $ State <chr> "Alabama", "Alabama", "Alabama", "Alabama", "Alabama", "Al…
## $ Year  <int> 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012…
## $ TFR   <dbl> 1.92205, 1.91695, 1.93785, 2.00555, 2.04290, 2.02050, 1.94…

Examine the Results

Let’s look at the results. First try side-by-side boxplots to look at the changes over time. Note that we have to cast Year as a factor to get our boxplots.

Solution

SYTFR %>% 
  ggplot(aes(x = factor(Year),y=TFR)) + geom_boxplot()

There are some distinct groups of years. For analysis purposes, I would group them as follows:

2003 - 2005 - Early
2006 - 2008 - Peak
2009 - 2010 - Decline (Possibly separate)
2012 - 2015 - Late

Solution

SYTFR %>% ggplot(aes(x= Year, y = TFR)) + geom_point()

Explanation?

Probably the great recession caused a drop in the birth rate.

The next step in our analysis is to introduce per capita personal income data from the Bureau of Economic Analysis. This is available in the file CA1.csv in Moodle. Import this data.

Solution

CA1 <- read_csv("~/Dropbox/RProjects/Fertility Study/CA1.csv")

## Parsed with column specification:
## cols(
##   .default = col_character(),
##   GeoFIPS = col_integer(),
##   Region = col_integer(),
##   LineCode = col_integer()
## )

## See spec(...) for full column specifications.

## Warning in rbind(names(probs), probs_f): number of columns of result is not
## a multiple of vector length (arg 1)

## Warning: 4 parsing failures.
## row # A tibble: 4 x 5 col     row col    expected  actual                         file                expected   <int> <chr>  <chr>     <chr>                          <chr>               actual 1  9595 GeoFI… an integ… Note: See the included footno… '~/Dropbox/RProjec… file 2  9596 GeoFI… an integ… CA1: Personal Income Summary:… '~/Dropbox/RProjec… row 3  9597 GeoFI… an integ… Last updated: November 17, 20… '~/Dropbox/RProjec… col 4  9598 GeoFI… an integ… Source: U.S. Department of Co… '~/Dropbox/RProjec…

Answer

Looking at the results of the import process, we can see that there are some invalid records at the bottom of the file. These can be eliminated by requiring that GeoFIPS be numeric. We also want to keep only the rows for statewide values. These can be indentified as having GeoName values containing the string “state”. The income data we want can be identified as having LineCode values of 3. In our output, we want only the name of the state and the income data in columns 8 through 54.

Solution

CA2 <- CA1 %>% 
  filter(LineCode == 3, str_detect(GeoName,"state")) %>%
  select(GeoName,8:54) %>%
  rename(State = GeoName)

Solution

Use View

Now we need to remove the extra text from the variable State. All rows have a string " state total" and some have an asterisk. These are removed in separate steps. The asterisk needs two leading backslashes because it has special significance in regular expressions. This is called “escaping.”

Solution

CA3 <- CA2 %>%
  mutate(State = gsub(" state total","",State)) %>% 
  mutate(State = gsub("\\*","",State))

Conclusion

Now we need to use the gather function from tidyr to put the column names indicating years into a column named Year with the income values from those columns in a single column named PCInc. In addition, we need to make Year and PCInc numeric. We only want data for the years 2003 through 2015.

Look at the documentation on gather() in Chapter 12 of RFDS.

Solution

CA4 <- CA3 %>% 
  gather(Year,PCInc,-1) %>% 
  mutate(Year = as.numeric(Year),
         PCInc = as.numeric(PCInc)) %>%   filter(Year >= 2003)
glimpse(CA4)

## Observations: 663
## Variables: 3
## $ State <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "California", …
## $ Year  <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003…
## $ PCInc <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 38187, 46…

Now we can join the fertility data with the income data and examine the relationship between the two.

AllData = inner_join(CA4,SYTFR)

## Joining, by = c("State", "Year")

glimpse(AllData)

## Observations: 663
## Variables: 4
## $ State <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "California", …
## $ Year  <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003…
## $ PCInc <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 38187, 46…
## $ TFR   <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480, 1.90…

We can now look at the relationship between per capita personal income and the TFR.

Do that with a scatterplot

Solution

AllData %>% ggplot(aes(x=PCInc,y=TFR)) + geom_point()

The plot suggests something counterituitive - Higher income leads to reduced fertility. This clashes with our explanation for the decline in fertility beginning with the great recession.

Let’s add time to this graphic by mapping color to Year.

Solution

AllData %>% ggplot(aes(x=PCInc,y=TFR,color=Year)) + geom_point()

It seems that there may be some correlation between time and our income variable. Review data on real personal income and the CPI in FRED. https://fred.stlouisfed.org/ is the link.

Let’s import the CPI data downloaded from FRED.

Solution

CPIData <- read_csv("~/Dropbox/RProjects/Fertility Study/CPIData.csv")

## Parsed with column specification:
## cols(
##   Year = col_integer(),
##   CPI = col_double()
## )

Now we need to join the CPI Data with AllData and adjust the per capita income data for inflation.

Solution

AllData2 = inner_join(AllData,CPIData)

## Joining, by = "Year"

AllData2 %>% mutate(RealPCInc = PCInc/CPI) -> AllData2
glimpse(AllData2)

## Observations: 663
## Variables: 6
## $ State     <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "Californi…
## $ Year      <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, …
## $ PCInc     <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 38187…
## $ TFR       <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480, …
## $ CPI       <dbl> 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 184,…
## $ RealPCInc <dbl> 144.0924, 193.4293, 153.0761, 138.4076, 191.4891, 190.…

Now redo the original scatterplot using the adjusted per capita income data.

Solution

AllData2 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Year)) + geom_point()

There is still a counterintuitive relationship. How can we explain this?

Let’s repeat the previous graph with a facet by year.

Solution

AllData2 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Year)) + geom_point() + geom_smooth() + facet_wrap(~Year)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Looking back at the side-by-side boxplot, recall the grouping we saw there.

2003 - 2005 - Early
2006 - 2008 - Peak
2009 - 2010 - Decline (Possibly separate)
2012 - 2015 - Late

We can use the case_when statement to develop a variable to capture this grouping.

Solution

AllData3 <- AllData2 %>% 
  mutate(Period = case_when(
                   .$Year < 2006 ~ "Early",
                   .$Year < 2009 ~ "Peak",
                   .$Year < 2012 ~ "Decline",
                   TRUE ~ "Late"),
         Period = factor(Period,levels=c("Early","Peak","Decline","Late"))
         )
str(AllData3)

## Classes 'tbl_df', 'tbl' and 'data.frame':    663 obs. of  7 variables:
##  $ State    : chr  "Alabama" "Alaska" "Arizona" "Arkansas" ...
##  $ Year     : num  2003 2003 2003 2003 2003 ...
##  $ PCInc    : num  26513 35591 28166 25467 35234 ...
##  $ TFR      : num  1.92 2.28 2.4 2.05 2.12 ...
##  $ CPI      : num  184 184 184 184 184 184 184 184 184 184 ...
##  $ RealPCInc: num  144 193 153 138 191 ...
##  $ Period   : Factor w/ 4 levels "Early","Peak",..: 1 1 1 1 1 1 1 1 1 1 ...

Now we can repeat the plot above with these groupings. We can also do a simple smoothing plot using the new variable to distinguish among periods.

Solution

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) + geom_point() + 
  geom_smooth() + facet_wrap(~Period)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Here is another look at this without a facet or the points.

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) +  
  geom_smooth()

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

Turning off the confidence interval shading might be better.

AllData3 %>% ggplot(aes(x=RealPCInc,y=TFR,color=Period)) +  
  geom_smooth(level=0.0)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

The impact of the peak years is clear. There is some separation of the curves for lower levels of RealPCInc, but the spearation is weaker at higher levles of RealPCInc.

Let’s try a regression model and include the factor Period. R will create dummy variables automatically to take care of the Period variable.

FertMod = lm(TFR~RealPCInc + Period,data = AllData3)
summary(FertMod)

## 
## Call:
## lm(formula = TFR ~ RealPCInc + Period, data = AllData3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.39463 -0.10693 -0.02544  0.09289  0.53061 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.4110913  0.0401444  60.061  < 2e-16 ***
## RealPCInc     -0.0021371  0.0002127 -10.047  < 2e-16 ***
## PeriodPeak     0.0802308  0.0199591   4.020 6.50e-05 ***
## PeriodDecline -0.0684196  0.0199052  -3.437 0.000625 ***
## PeriodLate    -0.1215957  0.0188969  -6.435 2.38e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1735 on 658 degrees of freedom
## Multiple R-squared:  0.2809, Adjusted R-squared:  0.2765 
## F-statistic: 64.26 on 4 and 658 DF,  p-value: < 2.2e-16

An Alternative

Let’s look at a few specific states in specific years.

str(AllData3)

## Classes 'tbl_df', 'tbl' and 'data.frame':    663 obs. of  7 variables:
##  $ State    : chr  "Alabama" "Alaska" "Arizona" "Arkansas" ...
##  $ Year     : num  2003 2003 2003 2003 2003 ...
##  $ PCInc    : num  26513 35591 28166 25467 35234 ...
##  $ TFR      : num  1.92 2.28 2.4 2.05 2.12 ...
##  $ CPI      : num  184 184 184 184 184 184 184 184 184 184 ...
##  $ RealPCInc: num  144 193 153 138 191 ...
##  $ Period   : Factor w/ 4 levels "Early","Peak",..: 1 1 1 1 1 1 1 1 1 1 ...

AllData3 %>% 
  
filter(State %in% c("Connecticut","Utah","Washington","Alabama"),
                    Year %in% c(2003,2008,2015)) %>%
  select(State,Year, RealPCInc,TFR) %>%
  arrange(State,Year)

## # A tibble: 12 x 4
##    State        Year RealPCInc   TFR
##    <chr>       <dbl>     <dbl> <dbl>
##  1 Alabama      2003      144.  1.92
##  2 Alabama      2008      155.  2.02
##  3 Alabama      2015      160.  1.83
##  4 Connecticut  2003      247.  1.90
##  5 Connecticut  2008      284.  1.85
##  6 Connecticut  2015      290.  1.60
##  7 Utah         2003      139.  2.62
##  8 Utah         2008      158.  2.65
##  9 Utah         2015      166.  2.29
## 10 Washington   2003      187.  1.91
## 11 Washington   2008      208.  2.02
## 12 Washington   2015      219.  1.81

The striking fact is that the different states have very different numbers for both of these variables. Moreover, the differences persist over time.

To make the numbers more comparable and more suitable for model building we frequently recast them in terms of percentage change from a base period. Here the base period is 2003. We will carry this out in distinct steps.

Step 1

Starting with AllData3, create a dataframe baseValues with the following variables.

State B_TFR - Value of TFR in 2003 B_RealPCInc - Value of RealPCInc in 2003

Answer

AllData3 %>% 
  filter(Year == 2003) %>% 
  mutate(B_TFR = TFR, B_RealPCInc = RealPCInc) %>% 
  select(State, B_TFR, B_RealPCInc) -> baseValues
glimpse(baseValues)

## Observations: 51
## Variables: 3
## $ State       <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "Califor…
## $ B_TFR       <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480…
## $ B_RealPCInc <dbl> 144.0924, 193.4293, 153.0761, 138.4076, 191.4891, 19…

Step 2

Join the baseValues table to AllData3 producing AllData4. Glimpse AllData4 to make sure it looks OK. In AllData4, create PD_RealPCInc PD_TFR. These are percentage differences from the base values.

Answer

AllData4 = inner_join(AllData3,baseValues)

## Joining, by = "State"

glimpse(AllData4)

## Observations: 663
## Variables: 9
## $ State       <chr> "Alabama", "Alaska", "Arizona", "Arkansas", "Califor…
## $ Year        <dbl> 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003, 2003…
## $ PCInc       <dbl> 26513, 35591, 28166, 25467, 35234, 35132, 45468, 381…
## $ TFR         <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480…
## $ CPI         <dbl> 184, 184, 184, 184, 184, 184, 184, 184, 184, 184, 18…
## $ RealPCInc   <dbl> 144.0924, 193.4293, 153.0761, 138.4076, 191.4891, 19…
## $ Period      <fct> Early, Early, Early, Early, Early, Early, Early, Ear…
## $ B_TFR       <dbl> 1.92205, 2.28325, 2.39805, 2.04710, 2.11665, 2.14480…
## $ B_RealPCInc <dbl> 144.0924, 193.4293, 153.0761, 138.4076, 191.4891, 19…

Fertility Study

Get Libraries and Raw Data

Parsing Errors ??

Solution

Create the Total Fertility Rate (TFR)

Examine the Results

Solution

Scatterplot.

Solution

Explanation?

Solution

Error Messages?

Answer

OK, Do that

Solution

Look at CA2

Solution

Do that

Solution

Examine

Conclusion

Do that

Solution

Do that with a scatterplot

Solution

Do that

Solution

Do that

Solution

Do that

Solution

Do that

Solution

Do that

Solution

Do that

Solution

Solution

An Alternative

Step 1

Answer

Step 2

Answer

Step 3

Answer

Step 4

Answer