chapter_one_second_update_smooth
Craig, Scott
2022-06-10
Table of Contents
preface
I. Maps
A. San Antonio
B. Austin
C. Dallas
II. PCA
A. Eigenvalues
B. Screeplot
C. Correlation Table
III. LPA
A. Normality Checks
B. Best model fit
i. Mclust
ii. Mplus Automation
C. Actual LPA
i. Mclust
a. Maps using Mclust
1. San Antonio
2. Austin
3. Dallas
ii.. Mplus Automation
a. Maps using Mplus Automation
1. San Antonio
2. Austin
3. Dallas
IV. Questions
preface
Some notes for this document:
WRT LPA, the main difference between Mclust and Mplus Automation
(seen within the tidyLPA part of this analysis), is that, while both use
MLE, the Mclust uses a more robust estimator IRT violations of
normality. It is also the default mechanism for use in the tidyLPA
package.
I had assumed that using PCA would produce results that would pass
normality tests….they don’t.
I’ve done some research about violations of normality and LPA, and from
what I’ve seen, statiticians think its abhorrent and social scientists
seem to think that it adds to the results?
I purposefully left some of the code visible as I think it helps when
viewing the various results.
I. Maps showing increasing number of issued bldg permits
A. San Antonio
Why do the titles for all of my maps end up in the first map? any
ideas?
B. Austin
C. Dallas
II. PCA
A. Eigenvalues
eigvar <- as.data.frame(eigenval1[,1:2])
print(eigvar)## eigenvalue percentage of variance
## comp 1 5.14387408 36.7419577
## comp 2 3.32067121 23.7190800
## comp 3 2.16624855 15.4732039
## comp 4 0.73810342 5.2721673
## comp 5 0.61289046 4.3777890
## comp 6 0.55693207 3.9780862
## comp 7 0.44559074 3.1827910
## comp 8 0.26488817 1.8920584
## comp 9 0.24949322 1.7820944
## comp 10 0.17503057 1.2502184
## comp 11 0.14555464 1.0396760
## comp 12 0.07933219 0.5666585
## comp 13 0.06826988 0.4876420
## comp 14 0.03312080 0.2365771B. Screeplot
### Examining the top three dimensions
###
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## y00_04 0.6489001 0.6082697 -0.05225295 0.141896912 -0.15848383
## y05_09 0.7084368 0.6604710 -0.04494231 0.055408625 -0.11546698
## y10_14 0.7256974 0.6278711 -0.04028562 -0.035566365 -0.08096414
## y15_19 0.6832288 0.6455477 -0.03450893 -0.004409448 -0.03571526
## inc_tot 0.4508568 0.5402738 -0.08119735 -0.072174637 0.57096953
## pnhw00 0.6703959 -0.4592231 -0.01664213 -0.480797623 0.05248946
III. LPA
A. Normality Checks
##
## Shapiro-Wilk normality test
##
## data: pca1_dim$dim1
## W = 0.56621, p-value < 2.2e-16##
## Shapiro-Wilk normality test
##
## data: pca1_dim$dim2
## W = 0.63969, p-value < 2.2e-16##
## Shapiro-Wilk normality test
##
## data: pca1_dim$dim3
## W = 0.67501, p-value < 2.2e-16B.Comparing Models
i. Mclust
# LPA
## comparing models
pca1_dim <- as.data.frame(pca1_dim)
pca1_dim%>%
dplyr::select(dim1,dim2,dim3) %>%
single_imputation() %>%
estimate_profiles(1:3,
variances = c("equal", "varying"),
covariances = c("zero", "varying")
) %>%
compare_solutions(statistics = c("AIC", "BIC"))## Compare tidyLPA solutions:
##
## Model Classes AIC BIC Warnings
## 1 1 34106.38 34142.03
## 1 2 33022.87 33082.29
## 1 3 31553.70 31636.89
## 6 1 34112.38 34165.85
## 6 2 Warning
## 6 3 Warning
##
## Best model according to AIC is Model 1 with 3 classes.
## Best model according to BIC is Model 1 with 3 classes.
##
## An analytic hierarchy process, based on the fit indices AIC, AWE, BIC, CLC, and KIC (Akogul & Erisoglu, 2017), suggests the best solution is Model 1 with 3 classes.ii. Mplus Automation
# LPA
## comparing models
pca1_dim%>%
dplyr::select(dim1,dim2,dim3) %>%
single_imputation() %>%
estimate_profiles(1:3,
variances = c("equal", "varying"),
covariances = c("zero", "varying"),
package = "MplusAutomation"
) %>%
compare_solutions(statistics = c("AIC", "BIC"))## Compare tidyLPA solutions:
##
## Model Classes AIC BIC Warnings
## 1 1 34106.38 34142.03
## 1 2 32116.38 32175.79
## 1 3 31290.20 31373.39
## 6 1 34112.38 34165.85
## 6 2 Warning
## 6 3 Warning
##
## Best model according to AIC is Model 1 with 3 classes.
## Best model according to BIC is Model 1 with 3 classes.
##
## An analytic hierarchy process, based on the fit indices AIC, AWE, BIC, CLC, and KIC (Akogul & Erisoglu, 2017), suggests the best solution is Model 1 with 3 classes.B. The actual LPA
i. Mclust
Table with number of classes
/
##
## 1 2 3
## 2417 271 124Class vs increasing bldg permits count and proportion
##
## 0 1 2 3
## 1 1980 241 149 47
## 2 23 103 103 42
## 3 5 9 49 61##
## 0 1 2 3
## 1 0.704 0.086 0.053 0.017
## 2 0.008 0.037 0.037 0.015
## 3 0.002 0.003 0.017 0.022ii. Maps of Mclust results
a. San Antonio
b. Austin
c. Dallas
ii. Mplus Automation results
#### Table with by class
##
## 1 2 3
## 176 2592 44Class vs increasing bldg permits count and proportion
##
## 0 1 2 3
## 1 16 39 59 62
## 2 1992 312 220 68
## 3 0 2 22 20##
## 0 1 2 3
## 1 0.006 0.014 0.021 0.022
## 2 0.708 0.111 0.078 0.024
## 3 0.000 0.001 0.008 0.007A.Maps of Mplus Automation outcome BEWARE, the classes changed, so the colors on the maps don’t represent the same things from the previous maps.
i. San Antonio
##
## austin dallas san_antonio
## 529 1748 535ii. Austin
iii. Dallas
## Questions?
When examining the SAT Mclust map I noticed the area up by the Rim
was showing ascending not gentrifying. I think this is because nothing
existed before that land got developed into stores and apartments. Is
there a way I can discriminate my analysis to exclude these
outcomes?
How does indentation work on HTML part of Rmarkdown? I’ve googled it and
still don’t find answers that work for me.
Overall, what do you think of the results? I was worried about moving
forward from here before we got a chance to discuss these results.