Temporal Processes - Lab 1
Jessica Kim jsk2225
October 7, 2016
Option 1. Trend Analysis
Prompt: Conduct a trend analysis of some variable of interest. Graph it and try different functional forms. Look for subgroup variation across time, too. Extra credit if you consider other variables as a means of explaining the trend. Explain all of your results.
Question
Do people who have kids have a more favorable view towards the harshness of criminal courts? Do people who have more kids have an even more favorable view?
Variables
Dependent Variable
Courts dealing with criminals: courts
In general, do you think the courts in this area deal too harshly or not harshly enough with criminals?
Possible responses:
1 Too harsh
2 Not harsh enough
3 About right
8 Don’t know
9 No answer
0 Not applicable
Explanatory Variables
1. Number of children: childs
How many children have you ever had? Please count all that were born alive at any time (including any you had from a previous marriage).
2. Highest year of school completed: educ
CODE HIGHEST DEGREE EARNED.
3. Respondent’s Sex: sex
Possible responses:
1 Male
2 Female
4. Think of self as liberal or conservative: polviews
A. We hear a lot of talk these days about liberals and conservatives. I’m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal–point 1–to extremely conservative–point 7. Where would you place yourself on this scale?
Possible responses:
1 Extremely liberal
2 Liberal
3 Slightly liberal
4 Moderate
5 Slghtly conservative
6 Conservative
7 Extremely conservative
8 Don’t know
9 No answer
0 Not applicable
Descriptive Analysis
# need to remove any missing values
courts_childs_nomiss <- na.omit(courts_childs) # That removed 57061 - 42111 = 14950 observations
# Now I can get average responses by year
courts_childs_nomiss_recodes <- courts_childs_nomiss %>%
mutate(courts_ordinal = ifelse(courts == 3, 2,
ifelse(courts == 2, 1,
ifelse(courts == 1, 3, courts))))
courts_childs_means <- aggregate(courts_childs_nomiss_recodes[, c(-3, -5)],
list(year = courts_childs_nomiss_recodes$year,
sex = courts_childs_nomiss_recodes$sex),
mean)| year | sex | courts | childs | educ | polviews | courts_ordinal |
|---|---|---|---|---|---|---|
| 1974 | 1 | 2.028481 | 2.246835 | 11.65506 | 4.094937 | 1.237342 |
| 1975 | 1 | 2.035836 | 2.003413 | 11.79352 | 4.010239 | 1.179181 |
| 1976 | 1 | 2.076547 | 1.903909 | 11.99511 | 4.008143 | 1.174267 |
| 1977 | 1 | 2.046326 | 1.931310 | 11.91214 | 4.041533 | 1.170926 |
| 1978 | 1 | 2.040678 | 1.877966 | 12.39661 | 4.083051 | 1.116949 |
| 1980 | 1 | 2.065436 | 1.817114 | 12.22483 | 4.149329 | 1.151007 |
| year | sex | courts | childs | educ | polviews | courts_ordinal | |
|---|---|---|---|---|---|---|---|
| 49 | 2002 | 2 | 2.096923 | 1.963077 | 13.33846 | 4.175385 | 1.318461 |
| 50 | 2004 | 2 | 2.100775 | 1.990698 | 13.50698 | 4.156589 | 1.398450 |
| 51 | 2006 | 2 | 2.119714 | 1.994795 | 13.41900 | 4.113207 | 1.375407 |
| 52 | 2008 | 2 | 2.094439 | 2.036726 | 13.46905 | 4.096537 | 1.390346 |
| 53 | 2010 | 2 | 2.048371 | 1.927937 | 13.52122 | 4.027641 | 1.436328 |
| 54 | 2012 | 2 | 2.070270 | 2.010811 | 13.65514 | 4.027027 | 1.491892 |
The courts and polviews variables included options of non responses, but the summary function shows that these responses were not included in the provided data. I recoded those variables to ordinal ones so that higher values in the courts variable indicate greater harshness sentiments toward criminal courts so that each value actually increases in harshness sentiment. Recoding the variable this way makes it an ordinal variable measuring a sentiment of harshness toward courts. I also omitted any missing values, which were about 26% of the observations.
To set up the data for a time trend analysis, I took the mean of the responses for views on the harshness of criminal courts, political ideology, the number of children birthed, and education years for each year in the dataset.
Individual Variable Trends
Based on the plots above, the average number of children birthed looks to have been steadily decreasing over this 40-year period. The overall difference between the average in 1972 (2.34 kids) and in 2000 (1.81 kids) is 0.53 which amounts to a 23 percent decrease in the average number of children ever had. I’m unsure as to why the trend for females is on average higher across the entire time period since having a child requires both sexes, but there could be differences of connection to one’s children, adoption, and in-vitro fertilization.
The other three variables have an upward trend over time. Education years look to have increased steadily from an average of less than high school to some college. Men had a greater mean for most years until about 2005 or so when the gap looks to have shrunk and then the average education years for women is now higher than that for men.
For overall responses on harshness of criminal courts, there is an initial decline, an increase that then stagnates, and then a marked increase from about 1995 on in the harshness sentiment. This is followed by a sharp decline around 2008. To be sure, the averaged data over time only varies from 2.02 to 2.13, but that may be meaningful on a 1 to 3 scale. The trends are not uniform by respondent sex until about the mid 1990s where both trend lines increase and then peak in the mid 2000s before decreasing markedly. Females did seem to believe courts were less harsh on average than men about the early 1980s, 1990, and in the late ’90s.
Finally, women have tended to be more liberal than men over the past 40 years and the overall trend is slightly upward towards a more liberal lean. The gap between responses by sex also seems to have gotten wider since the 1990s.
Inferential Analysis
Time on Court Harshness Sentiment
| Males Only | Females Only | |
|---|---|---|
| (Intercept) | -18.543*** (2.209) |
-14.540*** (2.308) |
| year | 0.010*** (0.001) |
0.008*** (0.001) |
| R-squared | 0.76 | 0.65 |
| adj. R-squared | 0.75 | 0.64 |
| sigma | 0.06 | 0.07 |
| F | 80.38 | 46.61 |
| p | 0.00 | 0.00 |
| N | 27 | 27 |
The OLS summaries above show coefficients for the same bivariate time trend model but with different subsets of data by respondent sex. The model is a slightly better fit to the Males Only model according to the R-squared statistic while the slope estimates for each additional year are practically identical. However the intercept is smaller for the Males Only model, suggesting that there is some heterogeneity from respondent sex.
The plot above shows a scatterplot of the average view of criminal courts as too harsh over years, color-coded by respondent sex. The lines overlaid are bivariate fitted lines estimating the effect of additional years on court harshness sentiment. The fitted lines are also color-coded by sex. The bivariate fits suggest that respondent sex may affect the slope of the fitted lines whereby males seem to have viewed the courts as more harsh over time at a faster rate than did females.
| No Interaction | With Interaction | |
|---|---|---|
| (Intercept) | 2.201*** (0.558) |
2.478*** (0.502) |
| poly(year, 2)1 | 0.857*** (0.154) |
2.605*** (0.495) |
| poly(year, 2)2 | 0.391*** (0.054) |
0.331*** (0.050) |
| childs | -0.155** (0.050) |
22.231*** (6.085) |
| educ | -0.054 (0.039) |
-0.041 (0.035) |
| polviews | 0.008 (0.084) |
-0.091 (0.080) |
| childs x year | -0.011*** (0.003) |
|
| R-squared | 0.89 | 0.92 |
| adj. R-squared | 0.88 | 0.91 |
| sigma | 0.04 | 0.04 |
| F | 80.42 | 86.77 |
| p | 0.00 | 0.00 |
| N | 54 | 54 |
The OLS summary output above show the coefficient estimates comparing the restricted and unrestricted model, where the unrestricted model included an interaction effect from average number of children and year. Both year and year-squared were significant at the 1% level with positive coefficients in a multivariate model that accounted for average number of children, average education years, and average political view. The adjusted R-squared statistic was quite high and shows that the model accounted for 88% of the data variation in the restricted model and 91% of it in the unrestricted model.
The average number of children was also a significant predictor of the average harshness view of courts, but the slope estimates are substantially different between the two models. The estimate in the restricted model shows that each additional child was associated with an average decrease of 0.16 on the harshness view of courts (p<0.01). However the estimate in the unrestricted model shows that it was associated with an average increase of 22.23 in the harshness view of courts. This is problematic because harshness was only measured at a ceiling of 3. This impractical estimate value may be due to the year variable ranging from 1972 to 2012.
Finally, the interaction term for average number of children and years was significant at the 0.1% level and has a negative direction. This suggests that greater average children had a moderating effect on the positive relationship between year and average views of courts as too harsh toward criminals.
F-Test
Model 1: courts_ordinal ~ poly(year, 2) + childs + educ + polviews
Model 2: courts_ordinal ~ poly(year, 2) + childs + educ + polviews + year:childs
| Res.Df | RSS | Df | Sum of Sq | F | Pr(>F) |
|---|---|---|---|---|---|
| 48 | 0.08284 | NA | NA | NA | NA |
| 47 | 0.06431 | 1 | 0.01852 | 13.54 | 0.0006014 |
The ANOVA results show that the unrestricted model is significantly different from the restricted model at the 0.001 level (i.e. the coefficients in the unrestricted model are significantly different from zero). The unrestricted model is therefore a better fit to the data.