DEM7223_Homework4
Karlerik Naslund
October 13, 2020
Homework 4 - Discreet Time Hazard Models
In this assignment, I will be creating discreet time hazard models with the ELS:2002 data.
The dependent variable, as usual, is community college entry after high school, the independent variables are as follows:
- Low SES (0 for high SES, 1 for low)
- Sex (Male/Female - as Factor)
- Race (Race/Ethnicity as defined by the ELS:2002 dataset - also as factor)
- Parents Educational level (as factor from "did not graduate high school" to "PhD")
- Grandparents Educational Level (same as parents educational level)
Here I create my variables:
#standardizing variable names
colnames(els)<-toupper(colnames(els))
#college entry variables
entry_variables<-els %>% select(STU_ID,SCH_ID,STRAT_ID,PSU,F2HS2P_P,F2PS1SEC,F3HS2PS1,F3PS1SEC,BYQXDATP,F1RDTLFT,BYSES1QU,F3QWT,BYP33,BYSEX,BYRACE,BYPARED,BYGPARED)
entry_variables<-entry_variables %>% mutate(F2_months_to_college=ifelse(F2HS2P_P<0,NA_real_,F2HS2P_P))
entry_variables<-entry_variables %>% mutate(F3_months_to_college=ifelse(F3HS2PS1<0,NA_real_,F3HS2PS1))
entry_variables<-entry_variables %>% mutate(F2_first_college_2_year=ifelse(F2PS1SEC==4,1,
ifelse(F2PS1SEC<0,NA_real_,
ifelse(F2PS1SEC<!0 & F2PS1SEC!=4,0,0))))
entry_variables<-entry_variables %>% mutate(F3_first_college_2_year=ifelse(F3PS1SEC==4,1,
ifelse(F3PS1SEC<0,NA_real_,
ifelse(F3PS1SEC<!0 & F3PS1SEC!=4,0,0))))
entry_variables_complete<-entry_variables %>% filter(!is.na(F3_first_college_2_year))
entry_variables_complete<-entry_variables_complete %>% mutate(TV_ENTERTAIN_HRS=ifelse(BYP33<0,NA,
ifelse(BYP33>=0 & BYP33<=3,0,
ifelse(BYP33>=4 & BYP33<=10,1,NA))))
entry_variables_complete<-entry_variables_complete %>% mutate(sex=ifelse(BYSEX==1,"Male",
ifelse(BYSEX==2,"Female",
ifelse(BYSEX<0,NA,NA))))
entry_variables_complete<-entry_variables_complete %>% mutate(parents_highest_ed=ifelse(BYPARED==1,"Did.Not.Graduate.HS",
ifelse(BYPARED==2,"HS.Grad.or.GED",
ifelse(BYPARED==3,"2.Year.School.No.Deg",
ifelse(BYPARED==4,"2.Year.School.Awarded.Deg",
ifelse(BYPARED==5,"4.Year.School.No.Deg",
ifelse(BYPARED==6,"4.Year.School.Awarded.Deg",
ifelse(BYPARED==7,"Masters.Degree",
ifelse(BYPARED==8,"PhD.or.other.doctorate",
ifelse(BYPARED<0,NA,NA))))))))))
entry_variables_complete<-entry_variables_complete %>% mutate(PARENT_HS_OR_LOWER=ifelse(parents_highest_ed=="Did.Not.Graduate.HS" | parents_highest_ed=="HS.Grad.or.GED",1,0))
entry_variables_complete<-entry_variables_complete %>% mutate(F3_UPDATED_MONTHS_TO_COLLEGE=ifelse(is.na(F3_months_to_college),21,F3_months_to_college))
entry_variables_complete<-entry_variables_complete %>% mutate(BY_LOW_SES=ifelse(BYSES1QU==1,1,
ifelse(BYSES1QU==2,1,
ifelse(BYSES1QU==3,0,
ifelse(BYSES1QU==4,0,
ifelse(BYSES1QU<0,NA_real_,0))))))
entry_variables_complete<-entry_variables_complete %>% mutate(race=ifelse(BYRACE==1,"Am.Indian",
ifelse(BYRACE==2,"Asian/Pacific",
ifelse(BYRACE==3,"Afr.American",
ifelse(BYRACE==4|BYRACE==5,"Hispanic",
ifelse(BYRACE==6,"2orMoreRace",
ifelse(BYRACE==7,"White",NA)))))))
entry_variables_complete<-entry_variables_complete %>% mutate(grandparents_highest_ed=ifelse(BYGPARED==1,"Did.Not.Graduate.HS",
ifelse(BYGPARED==2,"HS.Grad.or.GED",
ifelse(BYGPARED==3,"2.Year.School.No.Deg",
ifelse(BYGPARED==4,"2.Year.School.Awarded.Deg",
ifelse(BYGPARED==5,"4.Year.School.No.Deg",
ifelse(BYGPARED==6,"4.Year.School.Awarded.Deg",
ifelse(BYGPARED==7,"Masters.Degree",
ifelse(BYGPARED==8,"PhD.or.other.doctorate",
ifelse(BYGPARED<0,NA,NA))))))))))
entry_variables_complete<-entry_variables_complete %>% filter(!is.na(grandparents_highest_ed) & !is.na(race) & !is.na(PARENT_HS_OR_LOWER) & !is.na(sex))
entry_var_clean<-entry_variables_complete %>% select(STU_ID,STRAT_ID,PSU,F3_first_college_2_year,F3_UPDATED_MONTHS_TO_COLLEGE,sex,parents_highest_ed,grandparents_highest_ed,PARENT_HS_OR_LOWER,BY_LOW_SES,race,F3QWT)
entry_var_clean$sex<-as.factor(entry_var_clean$sex)
entry_var_clean$parents_highest_ed<-as.factor(entry_var_clean$parents_highest_ed)
entry_var_clean$grandparents_highest_ed<-as.factor(entry_var_clean$grandparents_highest_ed)
entry_var_clean$race<-as.factor(entry_var_clean$race)
# relevel factors
entry_var_clean$sex<-relevel(entry_var_clean$sex,ref = "Male")
entry_var_clean$parents_highest_ed<-relevel(entry_var_clean$parents_highest_ed,ref="HS.Grad.or.GED")
entry_var_clean$grandparents_highest_ed<-relevel(entry_var_clean$grandparents_highest_ed,ref="HS.Grad.or.GED")
entry_var_clean$race<-relevel(entry_var_clean$race,ref="White")Person-Period Data
Here, I create person-period data from the ELS:2002 dataset.
entry_var_wide<-dcast(entry_var_clean,STU_ID~F3_UPDATED_MONTHS_TO_COLLEGE,value.var="F3_first_college_2_year")
entry_var_wide[is.na(entry_var_wide)]<-0
entry_var_long<-reshape2::melt(entry_var_wide,id.vars="STU_ID",variable.name="time",value.name="cc_entry")
entry_var_long<-entry_var_long %>% arrange(STU_ID)
entry_var_long<-merge(entry_var_long,entry_var_clean,entry_var_clean[c(1:3,6:12)],by.x="STU_ID",by.y="STU_ID")
head(entry_var_long)## STU_ID time cc_entry STRAT_ID PSU F3_first_college_2_year
## 1 101101 0 0 101 1 1
## 2 101101 1 0 101 1 1
## 3 101101 2 0 101 1 1
## 4 101101 3 0 101 1 1
## 5 101101 4 0 101 1 1
## 6 101101 5 0 101 1 1
## F3_UPDATED_MONTHS_TO_COLLEGE sex parents_highest_ed
## 1 18 Female 4.Year.School.No.Deg
## 2 18 Female 4.Year.School.No.Deg
## 3 18 Female 4.Year.School.No.Deg
## 4 18 Female 4.Year.School.No.Deg
## 5 18 Female 4.Year.School.No.Deg
## 6 18 Female 4.Year.School.No.Deg
## grandparents_highest_ed PARENT_HS_OR_LOWER BY_LOW_SES race F3QWT
## 1 HS.Grad.or.GED 0 1 Hispanic 185.9702
## 2 HS.Grad.or.GED 0 1 Hispanic 185.9702
## 3 HS.Grad.or.GED 0 1 Hispanic 185.9702
## 4 HS.Grad.or.GED 0 1 Hispanic 185.9702
## 5 HS.Grad.or.GED 0 1 Hispanic 185.9702
## 6 HS.Grad.or.GED 0 1 Hispanic 185.9702As you can see, the data is now modified to where it is both long and divided by individual time points per subject (i.e, every time point is an observation).
Now I can create a survey design from the person-period data set:
des1<-svydesign(ids=~STU_ID,strata = ~STRAT_ID,weights = ~F3QWT,data = entry_var_long,nest=T)fit1<-svyglm(cc_entry~as.factor(time)+parents_highest_ed+grandparents_highest_ed+sex+race,design=des1,family=binomial(link=cloglog))This method turns the time (in months) into factors that become coefficients along with the other variables:
summary(fit1)##
## Call:
## svyglm(formula = cc_entry ~ as.factor(time) + parents_highest_ed +
## grandparents_highest_ed + sex + race, design = des1, family = binomial(link = cloglog))
##
## Survey design:
## svydesign(ids = ~STU_ID, strata = ~STRAT_ID, weights = ~F3QWT,
## data = entry_var_long, nest = T)
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -4.264725 0.137203 -31.083
## as.factor(time)1 0.031120 0.180079 0.173
## as.factor(time)2 1.733823 0.142374 12.178
## as.factor(time)3 2.476762 0.136393 18.159
## as.factor(time)4 0.239612 0.173679 1.380
## as.factor(time)5 -1.444871 0.314472 -4.595
## as.factor(time)6 -2.350539 0.412558 -5.697
## as.factor(time)7 0.031378 0.184916 0.170
## as.factor(time)8 0.069836 0.176375 0.396
## as.factor(time)9 -1.604870 0.316436 -5.072
## as.factor(time)10 -1.719350 0.352701 -4.875
## as.factor(time)11 -2.068528 0.376186 -5.499
## as.factor(time)12 -1.821119 0.344384 -5.288
## as.factor(time)13 -1.290512 0.272910 -4.729
## as.factor(time)14 -0.737724 0.215887 -3.417
## as.factor(time)15 0.347154 0.172327 2.015
## as.factor(time)16 -1.317365 0.280116 -4.703
## as.factor(time)17 -2.309596 0.493317 -4.682
## as.factor(time)18 -2.331290 0.434634 -5.364
## as.factor(time)19 -1.294900 0.262008 -4.942
## as.factor(time)20 -1.180477 0.261102 -4.521
## as.factor(time)21 1.844717 0.140740 13.107
## parents_highest_ed2.Year.School.Awarded.Deg 0.058152 0.059263 0.981
## parents_highest_ed2.Year.School.No.Deg 0.049737 0.059913 0.830
## parents_highest_ed4.Year.School.Awarded.Deg -0.416557 0.060835 -6.847
## parents_highest_ed4.Year.School.No.Deg -0.103100 0.063919 -1.613
## parents_highest_edDid.Not.Graduate.HS -0.016370 0.084864 -0.193
## parents_highest_edMasters.Degree -0.590304 0.082671 -7.140
## parents_highest_edPhD.or.other.doctorate -0.814680 0.124905 -6.522
## grandparents_highest_ed2.Year.School.Awarded.Deg -0.059857 0.076128 -0.786
## grandparents_highest_ed2.Year.School.No.Deg -0.017744 0.079377 -0.224
## grandparents_highest_ed4.Year.School.Awarded.Deg -0.243107 0.063125 -3.851
## grandparents_highest_ed4.Year.School.No.Deg -0.315656 0.100358 -3.145
## grandparents_highest_edDid.Not.Graduate.HS -0.008204 0.052254 -0.157
## grandparents_highest_edMasters.Degree -0.254248 0.088138 -2.885
## grandparents_highest_edPhD.or.other.doctorate -0.285042 0.117673 -2.422
## sexFemale -0.047322 0.036219 -1.307
## race2orMoreRace -0.000599 0.096624 -0.006
## raceAfr.American 0.021540 0.059388 0.363
## raceAm.Indian 0.020297 0.208075 0.098
## raceAsian/Pacific -0.071856 0.076107 -0.944
## raceHispanic 0.302828 0.050548 5.991
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## as.factor(time)1 0.862802
## as.factor(time)2 < 2e-16 ***
## as.factor(time)3 < 2e-16 ***
## as.factor(time)4 0.167739
## as.factor(time)5 4.40e-06 ***
## as.factor(time)6 1.26e-08 ***
## as.factor(time)7 0.865262
## as.factor(time)8 0.692151
## as.factor(time)9 4.03e-07 ***
## as.factor(time)10 1.11e-06 ***
## as.factor(time)11 3.94e-08 ***
## as.factor(time)12 1.27e-07 ***
## as.factor(time)13 2.30e-06 ***
## as.factor(time)14 0.000636 ***
## as.factor(time)15 0.043989 *
## as.factor(time)16 2.61e-06 ***
## as.factor(time)17 2.89e-06 ***
## as.factor(time)18 8.37e-08 ***
## as.factor(time)19 7.88e-07 ***
## as.factor(time)20 6.24e-06 ***
## as.factor(time)21 < 2e-16 ***
## parents_highest_ed2.Year.School.Awarded.Deg 0.326495
## parents_highest_ed2.Year.School.No.Deg 0.406470
## parents_highest_ed4.Year.School.Awarded.Deg 8.06e-12 ***
## parents_highest_ed4.Year.School.No.Deg 0.106785
## parents_highest_edDid.Not.Graduate.HS 0.847043
## parents_highest_edMasters.Degree 1.01e-12 ***
## parents_highest_edPhD.or.other.doctorate 7.32e-11 ***
## grandparents_highest_ed2.Year.School.Awarded.Deg 0.431734
## grandparents_highest_ed2.Year.School.No.Deg 0.823115
## grandparents_highest_ed4.Year.School.Awarded.Deg 0.000118 ***
## grandparents_highest_ed4.Year.School.No.Deg 0.001665 **
## grandparents_highest_edDid.Not.Graduate.HS 0.875254
## grandparents_highest_edMasters.Degree 0.003929 **
## grandparents_highest_edPhD.or.other.doctorate 0.015443 *
## sexFemale 0.191398
## race2orMoreRace 0.995054
## raceAfr.American 0.716844
## raceAm.Indian 0.922294
## raceAsian/Pacific 0.345124
## raceHispanic 2.17e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 0.9606816)
##
## Number of Fisher Scoring iterations: 9As we can see, many of the months-as-factors are significant in one way or another for affecting community college entry. There is a positive relationship between time and cc entry at the 2 and 3-month periods, while the other significant time periods have a negative effect upon community college entry -- aside from a small increase around month 15.
We can also run a regression of the outcome variable (cc entry) against the time variable, to see if there is any overall relationship between time and outcome:
fit.alternative.design<-svydesign(ids=~STU_ID,strata=~STRAT_ID,weights=~F3QWT,data=entry_var_clean,nest=T)
fit.alternative<-svyglm(formula=F3_first_college_2_year~F3_UPDATED_MONTHS_TO_COLLEGE,design=fit.alternative.design,family="binomial")
fit.0<-svyglm(F3_first_college_2_year~as.factor(F3_UPDATED_MONTHS_TO_COLLEGE)-1,design=fit.alternative.design,family="binomial")
summary(fit.alternative)##
## Call:
## svyglm(formula = F3_first_college_2_year ~ F3_UPDATED_MONTHS_TO_COLLEGE,
## design = fit.alternative.design, family = "binomial")
##
## Survey design:
## svydesign(ids = ~STU_ID, strata = ~STRAT_ID, weights = ~F3QWT,
## data = entry_var_clean, nest = T)
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.985099 0.037356 -26.37 <2e-16 ***
## F3_UPDATED_MONTHS_TO_COLLEGE 0.058620 0.004081 14.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 0.9997358)
##
## Number of Fisher Scoring iterations: 4It seems that there is a slight decrease in hazard over time.
General model vs. Alternative Time Specifications
Now we can test to see if the data is more suited for a general model, or some other time specification (squared, cubic, quadratic, etc.):
#squared
fit.sq<-svyglm(formula=F3_first_college_2_year~F3_UPDATED_MONTHS_TO_COLLEGE+I(F3_UPDATED_MONTHS_TO_COLLEGE^2),design=des1,family="binomial")
fit.cubic<-svyglm(formula=F3_first_college_2_year~F3_UPDATED_MONTHS_TO_COLLEGE+I(F3_UPDATED_MONTHS_TO_COLLEGE^2)+I(F3_UPDATED_MONTHS_TO_COLLEGE^3),design=des1,family="binomial")
fit.quadratic<-svyglm(formula=F3_first_college_2_year~F3_UPDATED_MONTHS_TO_COLLEGE+I(F3_UPDATED_MONTHS_TO_COLLEGE^2)+I(F3_UPDATED_MONTHS_TO_COLLEGE^3)+I(F3_UPDATED_MONTHS_TO_COLLEGE^4),design=des1,family="binomial")
fit.splines<-svyglm(formula=F3_first_college_2_year~ns(F3_UPDATED_MONTHS_TO_COLLEGE),design=des1,family="binomial")plot_alternative<-expand.grid(month=seq(1,21,1))
plot_alternative<-plot_alternative %>% mutate(F3_UPDATED_MONTHS_TO_COLLEGE=month)
plot_alternative$general<-predict(fit.0,newdata =plot_alternative,type="response")
plot_alternative$linear<-predict(fit.alternative,newdata=plot_alternative,type="response")
plot_alternative$squared<-predict(fit.sq,newdata=plot_alternative,type="response")
plot_alternative$cubed<-predict(fit.cubic,newdata=plot_alternative,type="response")
plot_alternative$quadratic<-predict(fit.quadratic,newdata=plot_alternative,type="response")
plot_alternative$splines<-predict(fit.splines,newdata=plot_alternative,type="response")
plot_alternative$F3_UPDATED_MONTHS_TO_COLLEGE<-NULL
plot_alternative## month general linear squared cubed quadratic splines
## 1 1 0.4262491 0.2836396 0.2513845 0.3190782 0.3510472 0.2718812
## 2 2 0.2729539 0.2957000 0.2806857 0.2980875 0.2919361 0.2842355
## 3 3 0.2841065 0.3080527 0.3099699 0.2912775 0.2776640 0.2969223
## 4 4 0.2439857 0.3206865 0.3387581 0.2963296 0.2936915 0.3099301
## 5 5 0.4226095 0.3335886 0.3666112 0.3117611 0.3323939 0.3232459
## 6 6 0.4252509 0.3467448 0.3931459 0.3365071 0.3877225 0.3368544
## 7 7 0.6346180 0.3601395 0.4180439 0.3694993 0.4522634 0.3507389
## 8 8 0.5212537 0.3737556 0.4410540 0.4093081 0.5172593 0.3648808
## 9 9 0.4472799 0.3875746 0.4619888 0.4539288 0.5746937 0.3792599
## 10 10 0.4490492 0.4015770 0.4807177 0.5007897 0.6192337 0.3938542
## 11 11 0.5875834 0.4157418 0.4971569 0.5469983 0.6485357 0.4086404
## 12 12 0.4737969 0.4300472 0.5112598 0.5897269 0.6622852 0.4235938
## 13 13 0.6184346 0.4444703 0.5230063 0.6265608 0.6611189 0.4386884
## 14 14 0.5653987 0.4589877 0.5323939 0.6556537 0.6461375 0.4538974
## 15 15 0.6952569 0.4735750 0.5394301 0.6756368 0.6191348 0.4691929
## 16 16 0.4681363 0.4882075 0.5441259 0.6853316 0.5832978 0.4845465
## 17 17 0.5134163 0.5028603 0.5464912 0.6833549 0.5438785 0.4999293
## 18 18 0.5223440 0.5175082 0.5465317 0.6677024 0.5082780 0.5153123
## 19 19 0.5537840 0.5321260 0.5442476 0.6354322 0.4854749 0.5306663
## 20 20 0.6164991 0.5466890 0.5396332 0.5827441 0.4855491 0.5459625
## 21 21 0.5142398 0.5611724 0.5326788 0.5061624 0.5199177 0.5611724After these parameters are created, we can graph them for visual inspection:
plot(general~month,plot_alternative,type="l",ylab="h(t)",xlab="Time (months)")
title(main="Hazard function from different time parameterizations")
lines(linear~month,plot_alternative,col=2,lwd=2)
lines(squared~month,plot_alternative,col=3,lwd=2)
lines(cubed~month,plot_alternative,col=4,lwd=2)
lines(quadratic~month,plot_alternative,col=5,lwd=2)
lines(splines~month,plot_alternative,col=6,lwd=2)
legend("bottomright",legend=c("General","Linear","Square","Cubic","Quadratic","Natural Spline"),col=1:6,lwd=1.5)
It seems that none of the different time parameterizations fit the general model very well.
We can see this mathematically in the AIC for all the models:
aic<-round(c(
fit1$deviance+2*length(fit1$coefficients),
fit.sq$deviance+2*length(fit.sq$coefficients),
fit.cubic$deviance+2*length(fit.cubic$coefficients),
fit.quadratic$deviance+2*length(fit.quadratic$coefficients),
fit.splines$deviance+2*length(fit.splines$coefficients),
fit.0$deviance+2*length(fit.0$coefficients)),2)
dif.aic<-round(aic-aic[6],2)
data.frame(model=c( "linear","square", "cubic", "quartic","spline", "general"),aic=aic,aic_dif=dif.aic)## model aic aic_dif
## 1 linear 24879.72 14099.88
## 2 square 240431.84 229652.00
## 3 cubic 238796.65 228016.81
## 4 quartic 237636.80 226856.96
## 5 spline 241021.58 230241.74
## 6 general 10779.84 0.00From this, we see that the general model is clearly preferred.
Interaction between two predictors
In light of the general model, I decided to add an additional independent variable to the model: an interaction term between "Parents Highest Education" and "Grandparents Highest Education". As both of these are significant in the general model, I imagine that they may have additional effects when interacting:
fit2<-svyglm(cc_entry~as.factor(time)+parents_highest_ed+grandparents_highest_ed+sex+race+(grandparents_highest_ed*parents_highest_ed),design=des1,family=binomial(link=cloglog))summary(fit2)##
## Call:
## svyglm(formula = cc_entry ~ as.factor(time) + parents_highest_ed +
## grandparents_highest_ed + sex + race + (grandparents_highest_ed *
## parents_highest_ed), design = des1, family = binomial(link = cloglog))
##
## Survey design:
## svydesign(ids = ~STU_ID, strata = ~STRAT_ID, weights = ~F3QWT,
## data = entry_var_long, nest = T)
##
## Coefficients:
## Estimate
## (Intercept) -4.260e+00
## as.factor(time)1 3.112e-02
## as.factor(time)2 1.735e+00
## as.factor(time)3 2.478e+00
## as.factor(time)4 2.397e-01
## as.factor(time)5 -1.445e+00
## as.factor(time)6 -2.351e+00
## as.factor(time)7 3.137e-02
## as.factor(time)8 6.986e-02
## as.factor(time)9 -1.605e+00
## as.factor(time)10 -1.719e+00
## as.factor(time)11 -2.069e+00
## as.factor(time)12 -1.821e+00
## as.factor(time)13 -1.291e+00
## as.factor(time)14 -7.377e-01
## as.factor(time)15 3.470e-01
## as.factor(time)16 -1.317e+00
## as.factor(time)17 -2.310e+00
## as.factor(time)18 -2.331e+00
## as.factor(time)19 -1.295e+00
## as.factor(time)20 -1.180e+00
## as.factor(time)21 1.845e+00
## parents_highest_ed2.Year.School.Awarded.Deg 2.464e-02
## parents_highest_ed2.Year.School.No.Deg 3.674e-02
## parents_highest_ed4.Year.School.Awarded.Deg -4.215e-01
## parents_highest_ed4.Year.School.No.Deg -1.600e-01
## parents_highest_edDid.Not.Graduate.HS -1.009e-02
## parents_highest_edMasters.Degree -5.060e-01
## parents_highest_edPhD.or.other.doctorate -4.199e-01
## grandparents_highest_ed2.Year.School.Awarded.Deg -4.460e-01
## grandparents_highest_ed2.Year.School.No.Deg 1.216e-01
## grandparents_highest_ed4.Year.School.Awarded.Deg -2.020e-01
## grandparents_highest_ed4.Year.School.No.Deg -2.583e-01
## grandparents_highest_edDid.Not.Graduate.HS -5.023e-02
## grandparents_highest_edMasters.Degree -1.625e-02
## grandparents_highest_edPhD.or.other.doctorate -3.144e-01
## sexFemale -4.741e-02
## race2orMoreRace -1.699e-02
## raceAfr.American 1.818e-02
## raceAm.Indian -6.634e-04
## raceAsian/Pacific -6.634e-02
## raceHispanic 3.065e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 4.537e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 4.400e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 5.383e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 2.239e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.Awarded.Deg -1.148e+01
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.Awarded.Deg 5.405e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.Awarded.Deg -1.846e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg -3.322e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg -1.232e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg -6.459e-02
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg -1.218e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.No.Deg -3.109e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.No.Deg -3.795e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.No.Deg -4.802e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 1.481e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 6.230e-02
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg -1.722e-02
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 5.097e-02
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.Awarded.Deg -6.496e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.Awarded.Deg -3.780e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.Awarded.Deg -6.740e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg -1.071e+00
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 3.344e-02
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg -2.778e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 1.754e-02
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.No.Deg 9.057e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.No.Deg 4.234e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.No.Deg -9.497e-03
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.259e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 6.575e-03
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS -1.532e-02
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.894e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edDid.Not.Graduate.HS 5.513e-02
## parents_highest_edMasters.Degree:grandparents_highest_edDid.Not.Graduate.HS 1.782e-02
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edDid.Not.Graduate.HS -7.100e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 1.589e-02
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edMasters.Degree -2.889e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree -2.170e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edMasters.Degree -2.985e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edMasters.Degree -1.162e+01
## parents_highest_edMasters.Degree:grandparents_highest_edMasters.Degree -4.147e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edMasters.Degree -1.012e+00
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 4.571e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate -2.003e-02
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate -2.308e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 7.028e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edPhD.or.other.doctorate 1.888e-01
## parents_highest_edMasters.Degree:grandparents_highest_edPhD.or.other.doctorate -3.156e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edPhD.or.other.doctorate -3.705e-01
## Std. Error
## (Intercept) 1.408e-01
## as.factor(time)1 1.801e-01
## as.factor(time)2 1.424e-01
## as.factor(time)3 1.364e-01
## as.factor(time)4 1.737e-01
## as.factor(time)5 3.145e-01
## as.factor(time)6 4.126e-01
## as.factor(time)7 1.849e-01
## as.factor(time)8 1.764e-01
## as.factor(time)9 3.164e-01
## as.factor(time)10 3.527e-01
## as.factor(time)11 3.762e-01
## as.factor(time)12 3.444e-01
## as.factor(time)13 2.729e-01
## as.factor(time)14 2.159e-01
## as.factor(time)15 1.723e-01
## as.factor(time)16 2.801e-01
## as.factor(time)17 4.933e-01
## as.factor(time)18 4.346e-01
## as.factor(time)19 2.620e-01
## as.factor(time)20 2.611e-01
## as.factor(time)21 1.408e-01
## parents_highest_ed2.Year.School.Awarded.Deg 8.180e-02
## parents_highest_ed2.Year.School.No.Deg 8.273e-02
## parents_highest_ed4.Year.School.Awarded.Deg 9.079e-02
## parents_highest_ed4.Year.School.No.Deg 9.097e-02
## parents_highest_edDid.Not.Graduate.HS 1.822e-01
## parents_highest_edMasters.Degree 1.304e-01
## parents_highest_edPhD.or.other.doctorate 2.237e-01
## grandparents_highest_ed2.Year.School.Awarded.Deg 2.782e-01
## grandparents_highest_ed2.Year.School.No.Deg 1.855e-01
## grandparents_highest_ed4.Year.School.Awarded.Deg 1.876e-01
## grandparents_highest_ed4.Year.School.No.Deg 2.909e-01
## grandparents_highest_edDid.Not.Graduate.HS 9.115e-02
## grandparents_highest_edMasters.Degree 2.406e-01
## grandparents_highest_edPhD.or.other.doctorate 4.691e-01
## sexFemale 3.612e-02
## race2orMoreRace 9.800e-02
## raceAfr.American 5.930e-02
## raceAm.Indian 2.123e-01
## raceAsian/Pacific 7.576e-02
## raceHispanic 5.054e-02
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 3.126e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 3.366e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 3.165e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 3.519e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.Awarded.Deg 6.743e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.Awarded.Deg 3.708e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.Awarded.Deg 5.717e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg 3.000e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg 2.336e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg 2.548e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg 2.991e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.No.Deg 5.862e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.No.Deg 3.923e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.No.Deg 5.300e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 2.408e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 2.574e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 2.221e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 2.422e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.Awarded.Deg 8.134e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.Awarded.Deg 2.770e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.Awarded.Deg 3.857e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg 5.225e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 3.970e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg 3.819e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 3.441e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.No.Deg 4.332e-01
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.No.Deg 3.775e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.No.Deg 5.257e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.453e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.487e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.763e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.613e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edDid.Not.Graduate.HS 2.103e-01
## parents_highest_edMasters.Degree:grandparents_highest_edDid.Not.Graduate.HS 2.694e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edDid.Not.Graduate.HS 5.488e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 3.160e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edMasters.Degree 3.494e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 2.937e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edMasters.Degree 3.620e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edMasters.Degree 1.044e+00
## parents_highest_edMasters.Degree:grandparents_highest_edMasters.Degree 3.347e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edMasters.Degree 4.657e-01
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 5.739e-01
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 6.617e-01
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 5.278e-01
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 5.175e-01
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edPhD.or.other.doctorate 8.770e-01
## parents_highest_edMasters.Degree:grandparents_highest_edPhD.or.other.doctorate 5.552e-01
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edPhD.or.other.doctorate 5.716e-01
## t value
## (Intercept) -30.254
## as.factor(time)1 0.173
## as.factor(time)2 12.181
## as.factor(time)3 18.164
## as.factor(time)4 1.380
## as.factor(time)5 -4.594
## as.factor(time)6 -5.697
## as.factor(time)7 0.170
## as.factor(time)8 0.396
## as.factor(time)9 -5.071
## as.factor(time)10 -4.874
## as.factor(time)11 -5.499
## as.factor(time)12 -5.288
## as.factor(time)13 -4.729
## as.factor(time)14 -3.417
## as.factor(time)15 2.014
## as.factor(time)16 -4.703
## as.factor(time)17 -4.682
## as.factor(time)18 -5.364
## as.factor(time)19 -4.942
## as.factor(time)20 -4.521
## as.factor(time)21 13.108
## parents_highest_ed2.Year.School.Awarded.Deg 0.301
## parents_highest_ed2.Year.School.No.Deg 0.444
## parents_highest_ed4.Year.School.Awarded.Deg -4.642
## parents_highest_ed4.Year.School.No.Deg -1.759
## parents_highest_edDid.Not.Graduate.HS -0.055
## parents_highest_edMasters.Degree -3.881
## parents_highest_edPhD.or.other.doctorate -1.877
## grandparents_highest_ed2.Year.School.Awarded.Deg -1.603
## grandparents_highest_ed2.Year.School.No.Deg 0.655
## grandparents_highest_ed4.Year.School.Awarded.Deg -1.076
## grandparents_highest_ed4.Year.School.No.Deg -0.888
## grandparents_highest_edDid.Not.Graduate.HS -0.551
## grandparents_highest_edMasters.Degree -0.068
## grandparents_highest_edPhD.or.other.doctorate -0.670
## sexFemale -1.313
## race2orMoreRace -0.173
## raceAfr.American 0.307
## raceAm.Indian -0.003
## raceAsian/Pacific -0.876
## raceHispanic 6.065
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 1.451
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 1.307
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 1.701
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 0.636
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.Awarded.Deg -17.022
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.Awarded.Deg 1.458
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.Awarded.Deg -0.323
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg -1.107
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg -0.527
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg -0.254
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg -0.407
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.No.Deg -0.530
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.No.Deg -0.967
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.No.Deg -0.906
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.615
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.242
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg -0.077
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.210
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.Awarded.Deg -0.799
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.Awarded.Deg -1.364
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.Awarded.Deg -1.747
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg -2.049
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.084
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg -0.727
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.051
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.No.Deg 2.091
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.No.Deg 1.122
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.No.Deg -0.018
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.866
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.044
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS -0.087
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 1.174
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edDid.Not.Graduate.HS 0.262
## parents_highest_edMasters.Degree:grandparents_highest_edDid.Not.Graduate.HS 0.066
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edDid.Not.Graduate.HS -1.294
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 0.050
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edMasters.Degree -0.827
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree -0.739
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edMasters.Degree -0.825
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edMasters.Degree -11.138
## parents_highest_edMasters.Degree:grandparents_highest_edMasters.Degree -1.239
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edMasters.Degree -2.174
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 0.796
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate -0.030
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate -0.437
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 1.358
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edPhD.or.other.doctorate 0.215
## parents_highest_edMasters.Degree:grandparents_highest_edPhD.or.other.doctorate -0.569
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edPhD.or.other.doctorate -0.648
## Pr(>|t|)
## (Intercept) < 2e-16
## as.factor(time)1 0.862826
## as.factor(time)2 < 2e-16
## as.factor(time)3 < 2e-16
## as.factor(time)4 0.167663
## as.factor(time)5 4.40e-06
## as.factor(time)6 1.26e-08
## as.factor(time)7 0.865294
## as.factor(time)8 0.692076
## as.factor(time)9 4.03e-07
## as.factor(time)10 1.11e-06
## as.factor(time)11 3.94e-08
## as.factor(time)12 1.27e-07
## as.factor(time)13 2.30e-06
## as.factor(time)14 0.000636
## as.factor(time)15 0.044093
## as.factor(time)16 2.61e-06
## as.factor(time)17 2.89e-06
## as.factor(time)18 8.37e-08
## as.factor(time)19 7.88e-07
## as.factor(time)20 6.25e-06
## as.factor(time)21 < 2e-16
## parents_highest_ed2.Year.School.Awarded.Deg 0.763247
## parents_highest_ed2.Year.School.No.Deg 0.656998
## parents_highest_ed4.Year.School.Awarded.Deg 3.50e-06
## parents_highest_ed4.Year.School.No.Deg 0.078677
## parents_highest_edDid.Not.Graduate.HS 0.955848
## parents_highest_edMasters.Degree 0.000105
## parents_highest_edPhD.or.other.doctorate 0.060510
## grandparents_highest_ed2.Year.School.Awarded.Deg 0.108913
## grandparents_highest_ed2.Year.School.No.Deg 0.512214
## grandparents_highest_ed4.Year.School.Awarded.Deg 0.281829
## grandparents_highest_ed4.Year.School.No.Deg 0.374591
## grandparents_highest_edDid.Not.Graduate.HS 0.581589
## grandparents_highest_edMasters.Degree 0.946166
## grandparents_highest_edPhD.or.other.doctorate 0.502782
## sexFemale 0.189358
## race2orMoreRace 0.862357
## raceAfr.American 0.759224
## raceAm.Indian 0.997507
## raceAsian/Pacific 0.381259
## raceHispanic 1.38e-09
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 0.146753
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 0.191207
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 0.089067
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg 0.524725
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.Awarded.Deg < 2e-16
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.Awarded.Deg 0.144943
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.Awarded.Deg 0.746743
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg 0.268153
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg 0.598059
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg 0.799857
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg 0.683828
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.No.Deg 0.595910
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.No.Deg 0.333492
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.No.Deg 0.364960
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.538545
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.808742
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.938228
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg 0.833371
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.Awarded.Deg 0.424545
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.Awarded.Deg 0.172472
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.Awarded.Deg 0.080620
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.040452
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.932870
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.466951
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg 0.959350
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.No.Deg 0.036561
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.No.Deg 0.262000
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.No.Deg 0.985586
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.386507
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.964730
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.930758
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS 0.240513
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edDid.Not.Graduate.HS 0.793268
## parents_highest_edMasters.Degree:grandparents_highest_edDid.Not.Graduate.HS 0.947275
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edDid.Not.Graduate.HS 0.195802
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 0.959897
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edMasters.Degree 0.408281
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree 0.460069
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edMasters.Degree 0.409668
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edMasters.Degree < 2e-16
## parents_highest_edMasters.Degree:grandparents_highest_edMasters.Degree 0.215374
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edMasters.Degree 0.029743
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 0.425791
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 0.975849
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate 0.661903
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate 0.174461
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edPhD.or.other.doctorate 0.829516
## parents_highest_edMasters.Degree:grandparents_highest_edPhD.or.other.doctorate 0.569704
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edPhD.or.other.doctorate 0.516831
##
## (Intercept) ***
## as.factor(time)1
## as.factor(time)2 ***
## as.factor(time)3 ***
## as.factor(time)4
## as.factor(time)5 ***
## as.factor(time)6 ***
## as.factor(time)7
## as.factor(time)8
## as.factor(time)9 ***
## as.factor(time)10 ***
## as.factor(time)11 ***
## as.factor(time)12 ***
## as.factor(time)13 ***
## as.factor(time)14 ***
## as.factor(time)15 *
## as.factor(time)16 ***
## as.factor(time)17 ***
## as.factor(time)18 ***
## as.factor(time)19 ***
## as.factor(time)20 ***
## as.factor(time)21 ***
## parents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_ed2.Year.School.No.Deg
## parents_highest_ed4.Year.School.Awarded.Deg ***
## parents_highest_ed4.Year.School.No.Deg .
## parents_highest_edDid.Not.Graduate.HS
## parents_highest_edMasters.Degree ***
## parents_highest_edPhD.or.other.doctorate .
## grandparents_highest_ed2.Year.School.Awarded.Deg
## grandparents_highest_ed2.Year.School.No.Deg
## grandparents_highest_ed4.Year.School.Awarded.Deg
## grandparents_highest_ed4.Year.School.No.Deg
## grandparents_highest_edDid.Not.Graduate.HS
## grandparents_highest_edMasters.Degree
## grandparents_highest_edPhD.or.other.doctorate
## sexFemale
## race2orMoreRace
## raceAfr.American
## raceAm.Indian
## raceAsian/Pacific
## raceHispanic ***
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg .
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.Awarded.Deg ***
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.Awarded.Deg
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_edMasters.Degree:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed2.Year.School.No.Deg
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.Awarded.Deg
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.Awarded.Deg .
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg *
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_ed4.Year.School.No.Deg
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_ed4.Year.School.No.Deg
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_ed4.Year.School.No.Deg *
## parents_highest_edMasters.Degree:grandparents_highest_ed4.Year.School.No.Deg
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_ed4.Year.School.No.Deg
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_edMasters.Degree:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edDid.Not.Graduate.HS
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edMasters.Degree
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edMasters.Degree
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edMasters.Degree
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edMasters.Degree ***
## parents_highest_edMasters.Degree:grandparents_highest_edMasters.Degree
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edMasters.Degree *
## parents_highest_ed2.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_ed2.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_ed4.Year.School.Awarded.Deg:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_ed4.Year.School.No.Deg:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_edDid.Not.Graduate.HS:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_edMasters.Degree:grandparents_highest_edPhD.or.other.doctorate
## parents_highest_edPhD.or.other.doctorate:grandparents_highest_edPhD.or.other.doctorate
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 0.960256)
##
## Number of Fisher Scoring iterations: 14The inclusion of the interaction terms has done something interesting: grandparents highest education (by themselves) are no longer significant. Yet, children of High School educated parents, who are themselves children of Master's degree-attaining parents, are significantly less likely to attend community college first out of High School.
This is interesting to me because it suggests that there is some kind of relationship between parental and grand-parental educational choices and the children's choice of future educational institution.
Hazard Plots
Here, I've created two hazard plots which detail the effects of race and parent's education upon community college entry after high school:
var_plot<-entry_var_long %>%
group_by(time,race) %>%
summarize(hz=mean(cc_entry,na.rm=T))## `summarise()` regrouping output by 'time' (override with `.groups` argument) ggplot(data=var_plot,aes(x=time,y=hz))+
geom_line(aes(group=factor(race),color=factor(race)))+
ggtitle(label="Hazard of CC Entry By Time and Race")
Here we see that Hispanics are more at-risk than African Americans to attend community college in the three months immediately following high school, but African Americans are more at risk during the 15-month bump.
This visual analysis is now repeated, but for parent's education level:
var_plot2<-entry_var_long %>%
group_by(time,parents_highest_ed) %>%
summarize(hz=mean(cc_entry,na.rm=T))## `summarise()` regrouping output by 'time' (override with `.groups` argument) ggplot(data=var_plot2,aes(x=time,y=hz))+
geom_line(aes(group=factor(parents_highest_ed),color=factor(parents_highest_ed)))+
ggtitle(label="Hazard of CC Entry By Time and Parents Highest Ed")
Interestingly, once again we see differences in risk categories at the 3 and 15 month periods. Students of parents who have a High School diploma or GED are at higher risk of CC attendence in month 15 than any other group, while in month 3, all groups with the exception of PhD's and Master degrees share similar risk profiles.
This is interesting to me as it suggests the primary groups at risk of community college entry are varying with time.
CONCLUSION
In this exercise we have learned the following:
there is a significant relationship between time after high school and community college entry
the general model is the most useful for describing the ELS:2002 data
the risk profiles of both race and parent's education vary by time
Thank you!