Final Project
Emmanuel Akinyele
2024-05-08
Introduction
I am interested in examining the school factors that encourage African American/Black high school boys to choose to major in Science, Technology, Engineering, and Mathematics (STEM) major in post secondary education in other to enter into the STEM profession (Professions like Engineer, Scientist, Computer Scientist, Information Technology, Medicine, etc). It is known that one’s professional career defines how successful they are and one needs to have knowledge and interest in that field to decide to pursue it. In a study by Kurban and Cabrera, they investigated “the role of cognitive and contextual factors affecting the process of high school students’ readiness for and consideration of an academic major in a STEM field” (Kurban & Cabrera, 2020). In their future research section of the article, they suggested to investigate the “extent to which school climate, school culture, and teacher expectations impact the STEM readiness and intention developmental process” (Kurban & Cabrera, 2020). The authors conducted Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) to discover five distinct latent factors (SES, Parental Involvment, Math Self-Efficacy, Science Self-Efficacy, and STEM Readiness) and four single indicators (Math Ability, Math Interest, Science Interest, and Intention to Major in STEM)
Problem Statement
I propose to investigate the extent to which school opportunities for students impact the STEM readiness and intention development process for Black boys using the High School Longitudinal Study of 2009 (HSLS:09).
Data and Variables
The High School Longitudinal Study of 2009 (HSLS:09) was a study conducted by the National Center for Education Statistics (NCES) as part of a series of secondary longitudinal studies. “The core research question for HSLS:09 explore secondary to postsecondary transition plans and the evolution of those plans; the paths into and out of science, technology, engineering, and mathematics; and the educational and social experiences that affect these shifts” (Ingels et al., 2011, p. iii). The longitudinal study takes the student as the fundamental unit of analysis. The base year occured in the fall term of 2009-10 School year, with a randomly selected sample of 9th graders in more than 900 public and private high schools (Ingels et al., 2011). There was a follow up study in spring of 2012 when the participants will be in the spring of the 11th grade.
Some questions on the student questionnaire allows to investigate the school environment through student, teacher, and administrator reports. This includes the extent to which schools are expected to provide special services to selected groups of students to compensate for limitations and poor performance. For example, including special services to assist those lagging in their understanding of mathematics and science is of interest in this study. (Ingels et al., 2011)
A subset of the publicly available data set is used, specifically using variables related to questions answered by school counselors and administrators.
knitr::opts_chunk$set(warning = FALSE)
setwd("~/UB/CEP525/FinalExam")
df <- read.csv("CEP525FinalDataSet.csv")
library(DT)## Warning: package 'DT' was built under R version 4.3.3library(vtable)## Warning: package 'vtable' was built under R version 4.3.3## Loading required package: kableExtra## Warning: package 'kableExtra' was built under R version 4.3.3df <- df[, !(names(df) %in% c("X.1", "X"))]
st(df)| Variable | N | Mean | Std. Dev. | Min | Pctl. 25 | Pctl. 75 | Max |
|---|---|---|---|---|---|---|---|
| x1sex | 23497 | ||||||
| … Female | 11524 | 49% | |||||
| … Male | 11973 | 51% | |||||
| x1black | 22938 | 0.16 | 0.37 | 0 | 0 | 0 | 1 |
| x1white | 22938 | 0.74 | 0.44 | 0 | 0 | 1 | 1 |
| x1hispanic | 22497 | 0.17 | 0.37 | 0 | 0 | 0 | 1 |
| x1locale | 23503 | ||||||
| … City | 6689 | 28% | |||||
| … Rural | 5559 | 24% | |||||
| … Suburb | 8467 | 36% | |||||
| … Town | 2788 | 12% | |||||
| x1region | 23503 | ||||||
| … Midwest | 6224 | 26% | |||||
| … Northeast | 3662 | 16% | |||||
| … South | 9587 | 41% | |||||
| … West | 4030 | 17% | |||||
| c1cluster | 23503 | 1.5 | 0.5 | 1 | 1 | 2 | 2 |
| c1indvcrs | 23503 | 2 | 0.22 | 1 | 2 | 2 | 2 |
| c1intern | 23503 | 1.4 | 0.49 | 1 | 1 | 2 | 2 |
| c1jobfair | 23503 | 1.3 | 0.45 | 1 | 1 | 2 | 2 |
| c1jobguide | 23503 | 1.3 | 0.46 | 1 | 1 | 2 | 2 |
| c1employer | 23503 | 1.6 | 0.49 | 1 | 1 | 2 | 2 |
| c1awareness | 23503 | 1.7 | 0.47 | 1 | 1 | 2 | 2 |
| c1careerunit | 23503 | 1.4 | 0.49 | 1 | 1 | 2 | 2 |
| c1workstudy | 23503 | 1.6 | 0.5 | 1 | 1 | 2 | 2 |
| c1careerday | 23503 | 1.4 | 0.49 | 1 | 1 | 2 | 2 |
| c1assemblies | 23503 | 1.4 | 0.49 | 1 | 1 | 2 | 2 |
| c1jobinfocmp | 23503 | 1.8 | 0.4 | 1 | 2 | 2 | 2 |
| c1jobinfonon | 23503 | 1.4 | 0.48 | 1 | 1 | 2 | 2 |
| c1hstowrkoth | 23503 | 1.2 | 0.43 | 1 | 1 | 1 | 2 |
| c1hstoworkno | 23503 | 1 | 0.15 | 1 | 1 | 1 | 2 |
| a1mspdlearn | 23503 | 1.6 | 0.48 | 1 | 1 | 2 | 2 |
| a1mspdintrst | 23503 | 1.4 | 0.48 | 1 | 1 | 2 | 2 |
| a1msother | 23503 | 1.2 | 0.41 | 1 | 1 | 1 | 2 |
| a1msnone | 23503 | 1 | 0.14 | 1 | 1 | 1 | 2 |
| a1g9summer | 23503 | 1.4 | 0.48 | 1 | 1 | 2 | 2 |
| a1g9overage | 23503 | 1.2 | 0.36 | 1 | 1 | 1 | 2 |
| a1g9communty | 23503 | 1.2 | 0.43 | 1 | 1 | 1 | 2 |
| a1g9blocksch | 23503 | 1.9 | 0.33 | 1 | 2 | 2 | 2 |
| a1g9double | 23503 | 1.6 | 0.49 | 1 | 1 | 2 | 2 |
| a1g9study | 23503 | 1.4 | 0.48 | 1 | 1 | 2 | 2 |
| a1g9teacher | 23503 | 1.4 | 0.48 | 1 | 1 | 2 | 2 |
One section of the counselor questionnaire focused on programs and services offered to students. Some questions pertained to enrichment courses, assistance for struggling students, dropout prevention programs, encouragement of the pursuit of mathematics and science education and employment, and assistance with the transition from high school to college or the workforce. “Other topics included the use of mathematics competency tests and options for failing students”(Ingels et al., 2011, p. 20)
My definition for “Opportunites for students” would be investigated with the following variables:
Counselor variables
| Variable Name | Varialbe Lable |
|---|---|
| c1cluster | C1 B30 Career Clusters/Pathways/Programs of Study (POS) offered |
| c1indvcrs | C1 B31 Student not enrolled in career Clusters, etc. may take course in program |
| c1intern | C1 B32A School offers internships with local employers |
| c1jobfair | C1 B32B School offers job fairs |
| c1jobguide | C1 B32C School offers Career guides or skills assessments |
| c1employer | C1 B32D School offers school/classroom presentations by local employers |
| c1awareness | C1 B32E School offers career awareness activities |
| c1careerunit | C1 B32G School offers career information units in subject-matter courses |
| c1workstudy | C1 B32H School offers exploratory work experience programs/co-op/workstudy/EBCE |
| c1careerday | C1 B32I School offers career days or nights |
| c1assemblies | C1 B32J School offers vocational oriented assemblies |
| c1jobinfocmp | C1 B32Q School offers computerized career information resources |
| c1jobinfonon | C1 B32R School offers non-computerized career information resources |
| c1hstowrkoth | C1 B32S School assists students with transition from HS to work in other ways |
| c1hstoworkno | C1 B32T School doesn’t assist students with transition from HS to work |
Administrator variables
| Variable Name | Variable Label |
|---|---|
| a1mspdlearn | A1 A25I Requires teacher prof development in how students learn math/science |
| a1mspdintrst | A1 A25J Requires teacher prof development in increasing interest in math/science |
| a1msother | A1 A25K Raises students math/science interest/achievement in another way |
| a1msnone | A1 A25L Doesn’t do any of these to raise math/science interest/achievement |
| a1g9summer | A1 A26A Offers pre-HS summer reading/math instructions for struggling 9th graders |
| a1g9overage | A1 A26B Offers learning communities for over-age student lacking HS prerequisite |
| a1g9communty | A1 A26C Offers 9th grade learning communities separate from rest of school |
| a1g9blocksch | A1 A26D Offers block scheduling to assist struggling 9th graders |
| a1g9double | A1 A26E Offers catch-up courses / double-dosing to assist struggling 9th graders |
| a1g9study | A1 A26F Offers study skill seminar/class for struggling 9th graders |
| a1g9teacher | A1 A26G Offers assistance for teachers working with struggling 9th graders |
Covariates
| Variable Name | Variable Label |
|---|---|
| x1sex | Sex of student (Male, Female) |
| x1black | Race of student is Black |
| x1white | Race of student is White |
| x1hispanic | Race of student is Hispanic |
| x1locale | Location where student resides (city, Rural, Suburb, Town) |
| x1region | Region where student resides (Midwest, Northeast, South, West) |
Sample size, description, excluded participants
In preparing the sample data, I downloaded the public available data set from the NCES website and then prep the data set as follows.
First, I choose the following variables from the HSLS:09 Student data set - sex, race (black, white, Hispanic), locale, region plus counselor variable of interest plus administrator variable of interest.
Next, I re coded the following variables - sex, locale and region. There were missing data within the data set and replaced these missed data with “NA”. The counselor and administrator variables were coded “O” for No and “1” for Yes. I had to recode the “0” to 1 (for No) and “1” to 2 (for Yes). The original variable type was character so I re coded them all to integer.
For missing values, I imputed with the mean of the column and rounded to the nearest whole integer. Then saved the final data set that needed to be used for latent class analysis (LCA)
The total sample size is 23503 with 32 variables
summary(as.factor(df$x1sex))## Female Male NA's
## 11524 11973 6summary (as.factor(df$x1black))## 0 1 NA's
## 19175 3763 565summary(as.factor(df$x1locale))## City Rural Suburb Town
## 6689 5559 8467 2788summary(as.factor(df$x1region))## Midwest Northeast South West
## 6224 3662 9587 4030Results
Multivariate Statistical Method
I will perform a Latent Class Analysis (LCA) on the variables responses by the school administrator and counselors to see the probability administrator and counselors answer yes to the “Opportunities for students”, and correlate it with gender, racial, place of residence (local and region) of the students.
knitr::opts_chunk$set(warning = FALSE)
library(poLCA)## Loading required package: scatterplot3d## Loading required package: MASSlibrary(vtable)
library(psych)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following object is masked from 'package:kableExtra':
##
## group_rows## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondf %>%
slice(1:10) %>%
kbl(caption = "Opportunities for students in HSLS:09 Dataset", digits = 1) %>%
kable_classic("hover", full_width = F, html_font = "Cambria")| x1sex | x1black | x1white | x1hispanic | x1locale | x1region | c1cluster | c1indvcrs | c1intern | c1jobfair | c1jobguide | c1employer | c1awareness | c1careerunit | c1workstudy | c1careerday | c1assemblies | c1jobinfocmp | c1jobinfonon | c1hstowrkoth | c1hstoworkno | a1mspdlearn | a1mspdintrst | a1msother | a1msnone | a1g9summer | a1g9overage | a1g9communty | a1g9blocksch | a1g9double | a1g9study | a1g9teacher |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Male | 0 | 1 | 0 | Rural | Midwest | 1 | 2 | 1 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 |
| Female | 0 | 1 | 0 | Rural | Northeast | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Female | 1 | 0 | 0 | Suburb | West | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 |
| Female | 0 | 1 | 0 | Suburb | South | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 1 |
| Male | 0 | 1 | 0 | City | South | 2 | 2 | 1 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 2 |
| Female | 0 | 1 | 0 | Rural | South | 2 | 2 | 1 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 |
| Female | 0 | 1 | 0 | Rural | Northeast | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| Male | 0 | 1 | 0 | Town | Northeast | 1 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 |
| Male | 0 | 1 | 0 | Town | South | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 |
| Female | 0 | 1 | 0 | City | Northeast | 2 | 2 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 |
Preparation for LCA (Select Variables)
As for the measure of opportunities for students (for struggling students), fifteen items related to opportunities for students were used to represent responses by the school counselor, and eleven items were used to represent responses by the school administrator.
Rationale for using latent class analysis (LCA) is a person-oriented approach where a number of distinctly separable classes or types of people or groups are identified based on the probabilities of answering to various responses to a certain construct.
f1 <- as.formula(cbind(c1cluster, c1indvcrs, c1intern, c1jobfair, c1jobguide, c1employer, c1awareness, c1careerunit, c1workstudy, c1careerday, c1assemblies,
c1jobinfocmp, c1jobinfonon, c1hstowrkoth, c1hstoworkno)~1)
f2 <- as.formula(cbind(a1mspdlearn, a1mspdintrst, a1msother, a1msnone, a1g9summer, a1g9overage, a1g9communty, a1g9blocksch, a1g9double, a1g9study, a1g9teacher)~1)max_II <- -100000
min_bic <- 100000
for (i in 1:4) {
lc <- poLCA(f1, df, nclass = i, maxiter = 3000,
tol = 1e-5, na.rm = FALSE, nrep = 10,
verbose = TRUE, calc.se = TRUE)
if(lc$bic < min_bic) {
min_bic <- lc$bic
LCA_best_model <- lc
}
}## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.4932 0.5068
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0489 0.9511
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.5709 0.4291
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.7213 0.2787
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.6897 0.3103
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.3934 0.6066
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.3341 0.6659
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.6101 0.3899
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.4348 0.5652
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.6049 0.3951
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.5795 0.4205
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.2024 0.7976
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.6445 0.3555
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.755 0.245
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.9783 0.0217
##
## Estimated class population shares
## 1
##
## Predicted class memberships (by modal posterior prob.)
## 1
##
## =========================================================
## Fit for 1 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 15
## residual degrees of freedom: 23488
## maximum log-likelihood: -202373.5
##
## AIC(1): 404777
## BIC(1): 404898
## G^2(1): 124537.1 (Likelihood ratio/deviance statistic)
## X^2(1): 3920120 (Chi-square goodness of fit)
##
## Model 1: llik = -187489.6 ... best llik = -187489.6
## Model 2: llik = -187489.6 ... best llik = -187489.6
## Model 3: llik = -187489.6 ... best llik = -187489.6
## Model 4: llik = -187489.6 ... best llik = -187489.6
## Model 5: llik = -187489.6 ... best llik = -187489.6
## Model 6: llik = -187489.6 ... best llik = -187489.6
## Model 7: llik = -187489.6 ... best llik = -187489.6
## Model 8: llik = -187489.6 ... best llik = -187489.6
## Model 9: llik = -187489.6 ... best llik = -187489.6
## Model 10: llik = -187489.6 ... best llik = -187489.6
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.6810 0.3190
## class 2: 0.2455 0.7545
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0375 0.9625
## class 2: 0.0640 0.9360
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.7624 0.2376
## class 2: 0.3186 0.6814
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.8888 0.1112
## class 2: 0.5003 0.4997
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.8201 0.1799
## class 2: 0.5177 0.4823
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.5443 0.4557
## class 2: 0.1943 0.8057
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.4679 0.5321
## class 2: 0.1578 0.8422
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.8323 0.1677
## class 2: 0.3171 0.6829
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.5173 0.4827
## class 2: 0.3260 0.6740
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.7731 0.2269
## class 2: 0.3832 0.6168
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.8236 0.1764
## class 2: 0.2577 0.7423
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.3217 0.6783
## class 2: 0.0450 0.9550
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.8692 0.1308
## class 2: 0.3482 0.6518
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.8681 0.1319
## class 2: 0.6058 0.3942
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.9618 0.0382
## class 2: 1.0000 0.0000
##
## Estimated class population shares
## 0.5687 0.4313
##
## Predicted class memberships (by modal posterior prob.)
## 0.5717 0.4283
##
## =========================================================
## Fit for 2 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 31
## residual degrees of freedom: 23472
## maximum log-likelihood: -187489.6
##
## AIC(2): 375041.2
## BIC(2): 375291.2
## G^2(2): 94769.25 (Likelihood ratio/deviance statistic)
## X^2(2): 773166.1 (Chi-square goodness of fit)
##
## Model 1: llik = -181024 ... best llik = -181024
## Model 2: llik = -181024 ... best llik = -181024
## Model 3: llik = -181024 ... best llik = -181024
## Model 4: llik = -181024 ... best llik = -181024
## Model 5: llik = -186446.1 ... best llik = -181024
## Model 6: llik = -181024 ... best llik = -181024
## Model 7: llik = -181024 ... best llik = -181024
## Model 8: llik = -184451.8 ... best llik = -181024
## Model 9: llik = -181024 ... best llik = -181024
## Model 10: llik = -184451.8 ... best llik = -181024
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.6189 0.3811
## class 2: 0.2659 0.7341
## class 3: 0.9787 0.0213
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0499 0.9501
## class 2: 0.0593 0.9407
## class 3: 0.0000 1.0000
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.7113 0.2887
## class 2: 0.3432 0.6568
## class 3: 1.0000 0.0000
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.8681 0.1319
## class 2: 0.5223 0.4777
## class 3: 1.0000 0.0000
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.7871 0.2129
## class 2: 0.5295 0.4705
## class 3: 0.9970 0.0030
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.7127 0.2873
## class 2: 0.1902 0.8098
## class 3: 0.0039 0.9961
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.6165 0.3835
## class 2: 0.1521 0.8479
## class 3: 0.0000 1.0000
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.8074 0.1926
## class 2: 0.3392 0.6608
## class 3: 1.0000 0.0000
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.6627 0.3373
## class 2: 0.3251 0.6749
## class 3: 0.0032 0.9968
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.7315 0.2685
## class 2: 0.4009 0.5991
## class 3: 0.9865 0.0135
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.7980 0.2020
## class 2: 0.2821 0.7179
## class 3: 1.0000 0.0000
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.4209 0.5791
## class 2: 0.0485 0.9515
## class 3: 0.0000 1.0000
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.8410 0.1590
## class 2: 0.3823 0.6177
## class 3: 1.0000 0.0000
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.8340 0.1660
## class 2: 0.6259 0.3741
## class 3: 1.0000 0.0000
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.9491 0.0509
## class 2: 1.0000 0.0000
## class 3: 1.0000 0.0000
##
## Estimated class population shares
## 0.4271 0.4655 0.1073
##
## Predicted class memberships (by modal posterior prob.)
## 0.4201 0.4712 0.1088
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 47
## residual degrees of freedom: 23456
## maximum log-likelihood: -181024
##
## AIC(3): 362142.1
## BIC(3): 362521.1
## G^2(3): 81838.14 (Likelihood ratio/deviance statistic)
## X^2(3): 494691.4 (Chi-square goodness of fit)
##
## Model 1: llik = -178320.5 ... best llik = -178320.5
## Model 2: llik = -178316.4 ... best llik = -178316.4
## Model 3: llik = -178333.6 ... best llik = -178316.4
## Model 4: llik = -178316.4 ... best llik = -178316.4
## Model 5: llik = -178316.4 ... best llik = -178316.4
## Model 6: llik = -178320.5 ... best llik = -178316.4
## Model 7: llik = -178316.4 ... best llik = -178316.4
## Model 8: llik = -178333.6 ... best llik = -178316.4
## Model 9: llik = -178333.6 ... best llik = -178316.4
## Model 10: llik = -178316.4 ... best llik = -178316.4
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.9886 0.0114
## class 2: 0.2249 0.7751
## class 3: 0.4859 0.5141
## class 4: 0.9845 0.0155
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0053 0.9947
## class 2: 0.0609 0.9391
## class 3: 0.0581 0.9419
## class 4: 0.0000 1.0000
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.9219 0.0781
## class 2: 0.2890 0.7110
## class 3: 0.6067 0.3933
## class 4: 1.0000 0.0000
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.9560 0.0440
## class 2: 0.4356 0.5644
## class 3: 0.8083 0.1917
## class 4: 1.0000 0.0000
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.9476 0.0524
## class 2: 0.5019 0.4981
## class 3: 0.7049 0.2951
## class 4: 0.9992 0.0008
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.9505 0.0495
## class 2: 0.1115 0.8885
## class 3: 0.5716 0.4284
## class 4: 0.0089 0.9911
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.9326 0.0674
## class 2: 0.1150 0.8850
## class 3: 0.4560 0.5440
## class 4: 0.0000 1.0000
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.9215 0.0785
## class 2: 0.2440 0.7560
## class 3: 0.7131 0.2869
## class 4: 1.0000 0.0000
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.9873 0.0127
## class 2: 0.2814 0.7186
## class 3: 0.5419 0.4581
## class 4: 0.0057 0.9943
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.9356 0.0644
## class 2: 0.3410 0.6590
## class 3: 0.6418 0.3582
## class 4: 0.9892 0.0108
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.9218 0.0782
## class 2: 0.1837 0.8163
## class 3: 0.6903 0.3097
## class 4: 1.0000 0.0000
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.8252 0.1748
## class 2: 0.0103 0.9897
## class 3: 0.2756 0.7244
## class 4: 0.0000 1.0000
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.9377 0.0623
## class 2: 0.2713 0.7287
## class 3: 0.7620 0.2380
## class 4: 1.0000 0.0000
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.9411 0.0589
## class 2: 0.5794 0.4206
## class 3: 0.7867 0.2133
## class 4: 1.0000 0.0000
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.7042 0.2958
## class 2: 1.0000 0.0000
## class 3: 1.0000 0.0000
## class 4: 1.0000 0.0000
##
## Estimated class population shares
## 0.0735 0.3175 0.5024 0.1067
##
## Predicted class memberships (by modal posterior prob.)
## 0.0701 0.3129 0.5089 0.1082
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 63
## residual degrees of freedom: 23440
## maximum log-likelihood: -178316.4
##
## AIC(4): 356758.8
## BIC(4): 357266.8
## G^2(4): 76422.84 (Likelihood ratio/deviance statistic)
## X^2(4): 468266.4 (Chi-square goodness of fit)
## LCA_best_model <- lc
LCA_best_model## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.9886 0.0114
## class 2: 0.2249 0.7751
## class 3: 0.4859 0.5141
## class 4: 0.9845 0.0155
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0053 0.9947
## class 2: 0.0609 0.9391
## class 3: 0.0581 0.9419
## class 4: 0.0000 1.0000
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.9219 0.0781
## class 2: 0.2890 0.7110
## class 3: 0.6067 0.3933
## class 4: 1.0000 0.0000
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.9560 0.0440
## class 2: 0.4356 0.5644
## class 3: 0.8083 0.1917
## class 4: 1.0000 0.0000
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.9476 0.0524
## class 2: 0.5019 0.4981
## class 3: 0.7049 0.2951
## class 4: 0.9992 0.0008
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.9505 0.0495
## class 2: 0.1115 0.8885
## class 3: 0.5716 0.4284
## class 4: 0.0089 0.9911
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.9326 0.0674
## class 2: 0.1150 0.8850
## class 3: 0.4560 0.5440
## class 4: 0.0000 1.0000
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.9215 0.0785
## class 2: 0.2440 0.7560
## class 3: 0.7131 0.2869
## class 4: 1.0000 0.0000
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.9873 0.0127
## class 2: 0.2814 0.7186
## class 3: 0.5419 0.4581
## class 4: 0.0057 0.9943
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.9356 0.0644
## class 2: 0.3410 0.6590
## class 3: 0.6418 0.3582
## class 4: 0.9892 0.0108
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.9218 0.0782
## class 2: 0.1837 0.8163
## class 3: 0.6903 0.3097
## class 4: 1.0000 0.0000
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.8252 0.1748
## class 2: 0.0103 0.9897
## class 3: 0.2756 0.7244
## class 4: 0.0000 1.0000
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.9377 0.0623
## class 2: 0.2713 0.7287
## class 3: 0.7620 0.2380
## class 4: 1.0000 0.0000
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.9411 0.0589
## class 2: 0.5794 0.4206
## class 3: 0.7867 0.2133
## class 4: 1.0000 0.0000
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.7042 0.2958
## class 2: 1.0000 0.0000
## class 3: 1.0000 0.0000
## class 4: 1.0000 0.0000
##
## Estimated class population shares
## 0.0735 0.3175 0.5024 0.1067
##
## Predicted class memberships (by modal posterior prob.)
## 0.0701 0.3129 0.5089 0.1082
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 63
## residual degrees of freedom: 23440
## maximum log-likelihood: -178316.4
##
## AIC(4): 356758.8
## BIC(4): 357266.8
## G^2(4): 76422.84 (Likelihood ratio/deviance statistic)
## X^2(4): 468266.4 (Chi-square goodness of fit)
## Brief Interpretation
For the best model, the probability for counselors to NOT provide opportunities for students should be: Class 3 > Class 1 > Class 2 > Class 4
fit.indices <- data.frame(
Model = c("Model 1", "Model 2", "Model 3", "Model 4"),
log_liklihood = c(-202373.5, -187489.6, -181024, -178316.4),
resid.df = c(23488, 23472, 23456, 23440),
BIC = c(404898, 375291.2, 362521.1, 357266.8),
AIC = c(404777, 375041.2, 362142.1, 356758.8),
likelihood_ratio = c(124537.1, 94769.25, 81838.14, 76422.84)
)
fit.indices %>%
kbl(caption = "Fit indices for Opportunites for students by School Counselor") %>%
kable_styling(full_width = F)| Model | log_liklihood | resid.df | BIC | AIC | likelihood_ratio |
|---|---|---|---|---|---|
| Model 1 | -202373.5 | 23488 | 404898.0 | 404777.0 | 124537.10 |
| Model 2 | -187489.6 | 23472 | 375291.2 | 375041.2 | 94769.25 |
| Model 3 | -181024.0 | 23456 | 362521.1 | 362142.1 | 81838.14 |
| Model 4 | -178316.4 | 23440 | 357266.8 | 356758.8 | 76422.84 |
max_II <- -100000
min_bic <- 100000
for (i in 1:4) {
lc2 <- poLCA(f2, df, nclass = i, maxiter = 3000,
tol = 1e-5, na.rm = FALSE, nrep = 10,
verbose = TRUE, calc.se = TRUE)
if(lc2$bic < min_bic) {
min_bic <- lc2$bic
LCA_best_model2 <- lc2
}
}## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.355 0.645
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.6436 0.3564
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.7827 0.2173
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 0.9811 0.0189
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.6469 0.3531
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 0.8496 0.1504
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.7526 0.2474
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.1222 0.8778
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.4038 0.5962
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.6392 0.3608
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.6227 0.3773
##
## Estimated class population shares
## 1
##
## Predicted class memberships (by modal posterior prob.)
## 1
##
## =========================================================
## Fit for 1 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 11
## residual degrees of freedom: 2036
## maximum log-likelihood: -138994.1
##
## AIC(1): 278010.2
## BIC(1): 278098.9
## G^2(1): 40874.66 (Likelihood ratio/deviance statistic)
## X^2(1): 151829.9 (Chi-square goodness of fit)
##
## Model 1: llik = -132319.4 ... best llik = -132319.4
## Model 2: llik = -132319.4 ... best llik = -132319.4
## Model 3: llik = -132319.4 ... best llik = -132319.4
## Model 4: llik = -132319.4 ... best llik = -132319.4
## Model 5: llik = -132319.4 ... best llik = -132319.4
## Model 6: llik = -132319.4 ... best llik = -132319.4
## Model 7: llik = -132319.4 ... best llik = -132319.4
## Model 8: llik = -132319.4 ... best llik = -132319.4
## Model 9: llik = -132319.4 ... best llik = -132319.4
## Model 10: llik = -132319.4 ... best llik = -132319.4
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.1604 0.8396
## class 2: 0.4520 0.5480
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.2981 0.7019
## class 2: 0.8157 0.1843
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.6893 0.3107
## class 2: 0.8292 0.1708
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 0.9970 0.0030
## class 2: 0.9732 0.0268
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.4582 0.5418
## class 2: 0.7409 0.2591
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 0.6233 0.3767
## class 2: 0.9623 0.0377
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.4739 0.5261
## class 2: 0.8915 0.1085
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0816 0.9184
## class 2: 0.1425 0.8575
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.3390 0.6610
## class 2: 0.4361 0.5639
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.4140 0.5860
## class 2: 0.7514 0.2486
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.1777 0.8223
## class 2: 0.8445 0.1555
##
## Estimated class population shares
## 0.3326 0.6674
##
## Predicted class memberships (by modal posterior prob.)
## 0.3301 0.6699
##
## =========================================================
## Fit for 2 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 23
## residual degrees of freedom: 2024
## maximum log-likelihood: -132319.4
##
## AIC(2): 264684.9
## BIC(2): 264870.4
## G^2(2): 27525.34 (Likelihood ratio/deviance statistic)
## X^2(2): 111654 (Chi-square goodness of fit)
##
## Model 1: llik = -131218.7 ... best llik = -131218.7
## Model 2: llik = -129611.7 ... best llik = -129611.7
## Model 3: llik = -129611.7 ... best llik = -129611.7
## Model 4: llik = -129611.7 ... best llik = -129611.7
## Model 5: llik = -131218.7 ... best llik = -129611.7
## Model 6: llik = -129611.7 ... best llik = -129611.7
## Model 7: llik = -129611.7 ... best llik = -129611.7
## Model 8: llik = -129611.7 ... best llik = -129611.7
## Model 9: llik = -129611.7 ... best llik = -129611.7
## Model 10: llik = -129611.7 ... best llik = -129611.7
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.1039 0.8961
## class 3: 0.6636 0.3364
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.9024 0.0976
## class 2: 0.2812 0.7188
## class 3: 0.8249 0.1751
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.9501 0.0499
## class 2: 0.7064 0.2936
## class 3: 0.7821 0.2179
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 1.0000 0.0000
## class 3: 0.9606 0.0394
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.9983 0.0017
## class 2: 0.4828 0.5172
## class 3: 0.6488 0.3512
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.6526 0.3474
## class 3: 0.9448 0.0552
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.9983 0.0017
## class 2: 0.5149 0.4851
## class 3: 0.8456 0.1544
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.0752 0.9248
## class 3: 0.1991 0.8009
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.0603 0.9397
## class 2: 0.3305 0.6695
## class 3: 0.5759 0.4241
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.9610 0.0390
## class 2: 0.4448 0.5552
## class 3: 0.6738 0.3262
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.9790 0.0210
## class 2: 0.2347 0.7653
## class 3: 0.7898 0.2102
##
## Estimated class population shares
## 0.164 0.3569 0.4791
##
## Predicted class memberships (by modal posterior prob.)
## 0.1756 0.3547 0.4696
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 35
## residual degrees of freedom: 2012
## maximum log-likelihood: -129611.7
##
## AIC(3): 259293.3
## BIC(3): 259575.6
## G^2(3): 22109.79 (Likelihood ratio/deviance statistic)
## X^2(3): 56826.11 (Chi-square goodness of fit)
##
## Model 1: llik = -128102.5 ... best llik = -128102.5
## Model 2: llik = -128102.5 ... best llik = -128102.5
## Model 3: llik = -128102.5 ... best llik = -128102.5
## Model 4: llik = -128102.5 ... best llik = -128102.5
## Model 5: llik = -128102.5 ... best llik = -128102.5
## Model 6: llik = -128102.5 ... best llik = -128102.5
## Model 7: llik = -128102.5 ... best llik = -128102.5
## Model 8: llik = -128102.5 ... best llik = -128102.5
## Model 9: llik = -128102.5 ... best llik = -128102.5
## Model 10: llik = -128102.5 ... best llik = -128102.5
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.1298 0.8702
## class 3: 1.0000 0.0000
## class 4: 0.1738 0.8262
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.9735 0.0265
## class 2: 0.3053 0.6947
## class 3: 1.0000 0.0000
## class 4: 0.4330 0.5670
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.9468 0.0532
## class 2: 0.6101 0.3899
## class 3: 0.7430 0.2570
## class 4: 0.8248 0.1752
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 1.000 0.000
## class 2: 1.000 0.000
## class 3: 0.928 0.072
## class 4: 1.000 0.000
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.9937 0.0063
## class 2: 0.4192 0.5808
## class 3: 0.6726 0.3274
## class 4: 0.5979 0.4021
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.4640 0.5360
## class 3: 0.9350 0.0650
## class 4: 0.9145 0.0855
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.9923 0.0077
## class 2: 0.3125 0.6875
## class 3: 0.8217 0.1783
## class 4: 0.8183 0.1817
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.0487 0.9513
## class 3: 0.1886 0.8114
## class 4: 0.1620 0.8380
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.0505 0.9495
## class 2: 0.1917 0.8083
## class 3: 0.5639 0.4361
## class 4: 0.5393 0.4607
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.9610 0.0390
## class 2: 0.3716 0.6284
## class 3: 0.6835 0.3165
## class 4: 0.6067 0.3933
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.9872 0.0128
## class 2: 0.0846 0.9154
## class 3: 0.7891 0.2109
## class 4: 0.6196 0.3804
##
## Estimated class population shares
## 0.1582 0.1861 0.2625 0.3932
##
## Predicted class memberships (by modal posterior prob.)
## 0.1562 0.1659 0.2941 0.3839
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 47
## residual degrees of freedom: 2000
## maximum log-likelihood: -128102.5
##
## AIC(4): 256299
## BIC(4): 256678
## G^2(4): 19091.43 (Likelihood ratio/deviance statistic)
## X^2(4): 37904.92 (Chi-square goodness of fit)
## LCA_best_model2 <- lc2
LCA_best_model2## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.1298 0.8702
## class 3: 1.0000 0.0000
## class 4: 0.1738 0.8262
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.9735 0.0265
## class 2: 0.3053 0.6947
## class 3: 1.0000 0.0000
## class 4: 0.4330 0.5670
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.9468 0.0532
## class 2: 0.6101 0.3899
## class 3: 0.7430 0.2570
## class 4: 0.8248 0.1752
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 1.000 0.000
## class 2: 1.000 0.000
## class 3: 0.928 0.072
## class 4: 1.000 0.000
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.9937 0.0063
## class 2: 0.4192 0.5808
## class 3: 0.6726 0.3274
## class 4: 0.5979 0.4021
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.4640 0.5360
## class 3: 0.9350 0.0650
## class 4: 0.9145 0.0855
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.9923 0.0077
## class 2: 0.3125 0.6875
## class 3: 0.8217 0.1783
## class 4: 0.8183 0.1817
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.0487 0.9513
## class 3: 0.1886 0.8114
## class 4: 0.1620 0.8380
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.0505 0.9495
## class 2: 0.1917 0.8083
## class 3: 0.5639 0.4361
## class 4: 0.5393 0.4607
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.9610 0.0390
## class 2: 0.3716 0.6284
## class 3: 0.6835 0.3165
## class 4: 0.6067 0.3933
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.9872 0.0128
## class 2: 0.0846 0.9154
## class 3: 0.7891 0.2109
## class 4: 0.6196 0.3804
##
## Estimated class population shares
## 0.1582 0.1861 0.2625 0.3932
##
## Predicted class memberships (by modal posterior prob.)
## 0.1562 0.1659 0.2941 0.3839
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## number of observations: 23503
## number of estimated parameters: 47
## residual degrees of freedom: 2000
## maximum log-likelihood: -128102.5
##
## AIC(4): 256299
## BIC(4): 256678
## G^2(4): 19091.43 (Likelihood ratio/deviance statistic)
## X^2(4): 37904.92 (Chi-square goodness of fit)
## Brief Interpretation
For the best model,
fit.indices2 <- data.frame(
Model = c("Model 1", "Model 2", "Model 3", "Model 4"),
log_liklihood = c(-138994.1, -132319.4, -129611.7, -128102.5),
resid.df = c(2036, 2024, 2012, 2000),
BIC = c(278098.9, 264870.4, 259575.6, 256678),
AIC = c(278010.2, 264684.9, 259293.3, 256299),
likelihood_ratio = c(40874.66, 27525.34, 22109.79, 19091.43)
)
fit.indices2 %>%
kbl(caption = "Fit indices for Opportunites for students by School Administrator") %>%
kable_styling(full_width = F)| Model | log_liklihood | resid.df | BIC | AIC | likelihood_ratio |
|---|---|---|---|---|---|
| Model 1 | -138994.1 | 2036 | 278098.9 | 278010.2 | 40874.66 |
| Model 2 | -132319.4 | 2024 | 264870.4 | 264684.9 | 27525.34 |
| Model 3 | -129611.7 | 2012 | 259575.6 | 259293.3 | 22109.79 |
| Model 4 | -128102.5 | 2000 | 256678.0 | 256299.0 | 19091.43 |
set.seed(112)
plot(LCA_best_model)
plot(LCA_best_model2)
Adding student gender as a covariates
f3 <- as.formula(cbind(c1cluster, c1indvcrs, c1intern, c1jobfair, c1jobguide, c1employer, c1awareness, c1careerunit, c1workstudy, c1careerday, c1assemblies,c1jobinfocmp, c1jobinfonon, c1hstowrkoth, c1hstoworkno)~x1sex)
f4 <- as.formula(cbind(a1mspdlearn, a1mspdintrst, a1msother, a1msnone, a1g9summer, a1g9overage, a1g9communty, a1g9blocksch, a1g9double, a1g9study, a1g9teacher)~x1sex)LCA <- poLCA(f3, data = df, nclass = 4, maxiter = 30000, nrep = 5)## Model 1: llik = -180983 ... best llik = -180983
## Model 2: llik = -178272.7 ... best llik = -178272.7
## Model 3: llik = -178272.7 ... best llik = -178272.7
## Model 4: llik = -178272.7 ... best llik = -178272.7
## Model 5: llik = -178272.7 ... best llik = -178272.7
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.9845 0.0155
## class 2: 0.9887 0.0113
## class 3: 0.2252 0.7748
## class 4: 0.4869 0.5131
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.0054 0.9946
## class 3: 0.0610 0.9390
## class 4: 0.0580 0.9420
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9220 0.0780
## class 3: 0.2895 0.7105
## class 4: 0.6075 0.3925
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9567 0.0433
## class 3: 0.4362 0.5638
## class 4: 0.8088 0.1912
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.9992 0.0008
## class 2: 0.9476 0.0524
## class 3: 0.5020 0.4980
## class 4: 0.7057 0.2943
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.0088 0.9912
## class 2: 0.9511 0.0489
## class 3: 0.1121 0.8879
## class 4: 0.5727 0.4273
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.9353 0.0647
## class 3: 0.1155 0.8845
## class 4: 0.4567 0.5433
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9219 0.0781
## class 3: 0.2447 0.7553
## class 4: 0.7140 0.2860
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 0.0057 0.9943
## class 2: 0.9886 0.0114
## class 3: 0.2819 0.7181
## class 4: 0.5425 0.4575
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.9892 0.0108
## class 2: 0.9374 0.0626
## class 3: 0.3417 0.6583
## class 4: 0.6422 0.3578
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9222 0.0778
## class 3: 0.1843 0.8157
## class 4: 0.6912 0.3088
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.8266 0.1734
## class 3: 0.0107 0.9893
## class 4: 0.2764 0.7236
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9381 0.0619
## class 3: 0.2721 0.7279
## class 4: 0.7628 0.2372
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.9421 0.0579
## class 3: 0.5797 0.4203
## class 4: 0.7871 0.2129
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.7013 0.2987
## class 3: 1.0000 0.0000
## class 4: 1.0000 0.0000
##
## Estimated class population shares
## 0.1066 0.0728 0.3186 0.502
##
## Predicted class memberships (by modal posterior prob.)
## 0.1081 0.0699 0.3151 0.5069
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## 2 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) -0.42871 0.05578 -7.686 0.000
## x1sexMale 0.09013 0.06868 1.312 0.189
## =========================================================
## 3 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 1.12855 0.03572 31.590 0.000
## x1sexMale -0.06607 0.04797 -1.377 0.168
## =========================================================
## 4 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 1.56849 0.03357 46.729 0.000
## x1sexMale -0.03650 0.04569 -0.799 0.424
## =========================================================
## number of observations: 23497
## number of estimated parameters: 66
## residual degrees of freedom: 23431
## maximum log-likelihood: -178272.7
##
## AIC(4): 356677.4
## BIC(4): 357209.7
## X^2(4): 468140.2 (Chi-square goodness of fit)
##
## ALERT: estimation algorithm automatically restarted with new initial values
## probs.start <- LCA$probs.start
plot(LCA)
LCA2 <- poLCA(f4, data = df, nclass = 4, maxiter = 30000, nrep = 5)## Model 1: llik = -132296.9 ... best llik = -132296.9
## Model 2: llik = -128084.6 ... best llik = -128084.6
## Model 3: llik = -128084.6 ... best llik = -128084.6
## Model 4: llik = -138969 ... best llik = -128084.6
## Model 5: llik = -138969 ... best llik = -128084.6
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.1298 0.8702
## class 3: 1.0000 0.0000
## class 4: 0.1737 0.8263
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.9738 0.0262
## class 2: 0.3053 0.6947
## class 3: 1.0000 0.0000
## class 4: 0.4328 0.5672
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.9467 0.0533
## class 2: 0.6100 0.3900
## class 3: 0.7430 0.2570
## class 4: 0.8247 0.1753
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 1.0000 0.0000
## class 3: 0.9281 0.0719
## class 4: 1.0000 0.0000
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.9938 0.0062
## class 2: 0.4191 0.5809
## class 3: 0.6726 0.3274
## class 4: 0.5980 0.4020
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.4638 0.5362
## class 3: 0.9350 0.0650
## class 4: 0.9144 0.0856
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.9923 0.0077
## class 2: 0.3122 0.6878
## class 3: 0.8217 0.1783
## class 4: 0.8183 0.1817
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0000 1.0000
## class 2: 0.0487 0.9513
## class 3: 0.1886 0.8114
## class 4: 0.1618 0.8382
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.0508 0.9492
## class 2: 0.1916 0.8084
## class 3: 0.5639 0.4361
## class 4: 0.5390 0.4610
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.9609 0.0391
## class 2: 0.3714 0.6286
## class 3: 0.6835 0.3165
## class 4: 0.6068 0.3932
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.9873 0.0127
## class 2: 0.0845 0.9155
## class 3: 0.7891 0.2109
## class 4: 0.6194 0.3806
##
## Estimated class population shares
## 0.1579 0.186 0.2626 0.3935
##
## Predicted class memberships (by modal posterior prob.)
## 0.156 0.1659 0.2942 0.3839
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## 2 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.18072 0.04557 3.966 0.000
## x1sexMale -0.03346 0.05061 -0.661 0.509
## =========================================================
## 3 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.52177 0.03494 14.935 0.000
## x1sexMale -0.02561 0.04463 -0.574 0.566
## =========================================================
## 4 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.94016 0.03986 23.584 0.000
## x1sexMale -0.05350 0.04562 -1.173 0.241
## =========================================================
## number of observations: 23497
## number of estimated parameters: 50
## residual degrees of freedom: 1997
## maximum log-likelihood: -128084.6
##
## AIC(4): 256269.2
## BIC(4): 256672.5
## X^2(4): 37908.8 (Chi-square goodness of fit)
##
## ALERT: estimation algorithm automatically restarted with new initial values
## probs.start <- LCA2$probs.start
plot(LCA2)
LCA with covariates - student gender, race, locale and region
f5 <- as.formula(cbind(c1cluster, c1indvcrs, c1intern, c1jobfair, c1jobguide, c1employer, c1awareness, c1careerunit, c1workstudy, c1careerday, c1assemblies,c1jobinfocmp, c1jobinfonon, c1hstowrkoth, c1hstoworkno)~x1sex+x1black+x1white+x1hispanic+x1locale+x1region)
f6 <- as.formula(cbind(a1mspdlearn, a1mspdintrst, a1msother, a1msnone, a1g9summer, a1g9overage, a1g9communty, a1g9blocksch, a1g9double, a1g9study, a1g9teacher)~x1sex+x1black+x1white+x1hispanic+x1locale+x1region)LCA3 <- poLCA(f5, data = df, nclass = 4, maxiter = 30000, nrep = 5)## Model 1: llik = -172563.6 ... best llik = -172563.6
## Model 2: llik = -167186.3 ... best llik = -167186.3
## Model 3: llik = -167186.3 ... best llik = -167186.3
## Model 4: llik = -167186.3 ... best llik = -167186.3
## Model 5: llik = -167304 ... best llik = -167186.3
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $c1cluster
## Pr(1) Pr(2)
## class 1: 0.9897 0.0103
## class 2: 0.9845 0.0155
## class 3: 0.2283 0.7717
## class 4: 0.4980 0.5020
##
## $c1indvcrs
## Pr(1) Pr(2)
## class 1: 0.0054 0.9946
## class 2: 0.0000 1.0000
## class 3: 0.0605 0.9395
## class 4: 0.0546 0.9454
##
## $c1intern
## Pr(1) Pr(2)
## class 1: 0.9234 0.0766
## class 2: 1.0000 0.0000
## class 3: 0.2953 0.7047
## class 4: 0.6160 0.3840
##
## $c1jobfair
## Pr(1) Pr(2)
## class 1: 0.9666 0.0334
## class 2: 1.0000 0.0000
## class 3: 0.4411 0.5589
## class 4: 0.8160 0.1840
##
## $c1jobguide
## Pr(1) Pr(2)
## class 1: 0.9543 0.0457
## class 2: 0.9991 0.0009
## class 3: 0.5059 0.4941
## class 4: 0.7099 0.2901
##
## $c1employer
## Pr(1) Pr(2)
## class 1: 0.9537 0.0463
## class 2: 0.0022 0.9978
## class 3: 0.1175 0.8825
## class 4: 0.5816 0.4184
##
## $c1awareness
## Pr(1) Pr(2)
## class 1: 0.9399 0.0601
## class 2: 0.0000 1.0000
## class 3: 0.1188 0.8812
## class 4: 0.4623 0.5377
##
## $c1careerunit
## Pr(1) Pr(2)
## class 1: 0.9261 0.0739
## class 2: 1.0000 0.0000
## class 3: 0.2581 0.7419
## class 4: 0.7187 0.2813
##
## $c1workstudy
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 0.0002 0.9998
## class 3: 0.2866 0.7134
## class 4: 0.5464 0.4536
##
## $c1careerday
## Pr(1) Pr(2)
## class 1: 0.9477 0.0523
## class 2: 0.9891 0.0109
## class 3: 0.3508 0.6492
## class 4: 0.6447 0.3553
##
## $c1assemblies
## Pr(1) Pr(2)
## class 1: 0.9307 0.0693
## class 2: 1.0000 0.0000
## class 3: 0.1886 0.8114
## class 4: 0.7010 0.2990
##
## $c1jobinfocmp
## Pr(1) Pr(2)
## class 1: 0.8393 0.1607
## class 2: 0.0000 1.0000
## class 3: 0.0157 0.9843
## class 4: 0.2808 0.7192
##
## $c1jobinfonon
## Pr(1) Pr(2)
## class 1: 0.9387 0.0613
## class 2: 1.0000 0.0000
## class 3: 0.2794 0.7206
## class 4: 0.7726 0.2274
##
## $c1hstowrkoth
## Pr(1) Pr(2)
## class 1: 0.9495 0.0505
## class 2: 1.0000 0.0000
## class 3: 0.5807 0.4193
## class 4: 0.7908 0.2092
##
## $c1hstoworkno
## Pr(1) Pr(2)
## class 1: 0.6731 0.3269
## class 2: 1.0000 0.0000
## class 3: 1.0000 0.0000
## class 4: 1.0000 0.0000
##
## Estimated class population shares
## 0.0692 0.1016 0.3293 0.4999
##
## Predicted class memberships (by modal posterior prob.)
## 0.0708 0.104 0.3284 0.4969
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## 2 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.16919 0.13567 1.247 0.212
## x1sexMale -0.10118 0.07361 -1.375 0.169
## x1black -0.09856 0.11575 -0.852 0.394
## x1white -0.22175 0.09643 -2.300 0.021
## x1hispanic 0.46481 0.10536 4.411 0.000
## x1localeRural 0.77854 0.12282 6.339 0.000
## x1localeSuburb 1.00359 0.09471 10.596 0.000
## x1localeTown 0.37831 0.14497 2.610 0.009
## x1regionNortheast 0.81378 0.14419 5.644 0.000
## x1regionSouth -0.40145 0.10213 -3.931 0.000
## x1regionWest -0.40066 0.12935 -3.097 0.002
## =========================================================
## 3 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.93077 0.12037 7.733 0.000
## x1sexMale -0.16552 0.06476 -2.556 0.011
## x1black 0.12657 0.10392 1.218 0.223
## x1white 0.07192 0.08745 0.822 0.411
## x1hispanic 0.18632 0.09632 1.934 0.053
## x1localeRural 1.32780 0.10881 12.203 0.000
## x1localeSuburb 0.94142 0.08531 11.035 0.000
## x1localeTown 1.02538 0.12559 8.165 0.000
## x1regionNortheast 0.53553 0.13639 3.926 0.000
## x1regionSouth -0.14909 0.09025 -1.652 0.099
## x1regionWest -0.21285 0.11640 -1.829 0.067
## =========================================================
## 4 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 1.58079 0.12069 13.098 0.000
## x1sexMale -0.11699 0.06511 -1.797 0.072
## x1black 0.08705 0.10446 0.833 0.405
## x1white 0.05584 0.08766 0.637 0.524
## x1hispanic 0.28351 0.09669 2.932 0.003
## x1localeRural 1.29271 0.11082 11.665 0.000
## x1localeSuburb 1.04618 0.08605 12.159 0.000
## x1localeTown 0.94291 0.12661 7.447 0.000
## x1regionNortheast 0.21312 0.13709 1.555 0.120
## x1regionSouth -0.52924 0.09042 -5.853 0.000
## x1regionWest -0.58730 0.11671 -5.032 0.000
## =========================================================
## number of observations: 22046
## number of estimated parameters: 93
## residual degrees of freedom: 21953
## maximum log-likelihood: -167186.3
##
## AIC(4): 334558.6
## BIC(4): 335302.6
## X^2(4): 445957.8 (Chi-square goodness of fit)
##
## ALERT: estimation algorithm automatically restarted with new initial values
## probs.start <- LCA3$probs.start
plot(LCA3)
LCA4 <- poLCA(f6, data = df, nclass = 4, maxiter = 30000, nrep = 5)## Model 1: llik = -119605.3 ... best llik = -119605.3
## Model 2: llik = -120221.7 ... best llik = -119605.3
## Model 3: llik = -129656.2 ... best llik = -119605.3
## Model 4: llik = -120473.9 ... best llik = -119605.3
## Model 5: llik = -121543 ... best llik = -119605.3
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $a1mspdlearn
## Pr(1) Pr(2)
## class 1: 0.120 0.880
## class 2: 0.000 1.000
## class 3: 0.184 0.816
## class 4: 1.000 0.000
##
## $a1mspdintrst
## Pr(1) Pr(2)
## class 1: 0.3231 0.6769
## class 2: 0.9728 0.0272
## class 3: 0.4390 0.5610
## class 4: 1.0000 0.0000
##
## $a1msother
## Pr(1) Pr(2)
## class 1: 0.6432 0.3568
## class 2: 0.9505 0.0495
## class 3: 0.8171 0.1829
## class 4: 0.7461 0.2539
##
## $a1msnone
## Pr(1) Pr(2)
## class 1: 1.0000 0.0000
## class 2: 1.0000 0.0000
## class 3: 1.0000 0.0000
## class 4: 0.9282 0.0718
##
## $a1g9summer
## Pr(1) Pr(2)
## class 1: 0.4408 0.5592
## class 2: 1.0000 0.0000
## class 3: 0.6033 0.3967
## class 4: 0.6690 0.3310
##
## $a1g9overage
## Pr(1) Pr(2)
## class 1: 0.4934 0.5066
## class 2: 1.0000 0.0000
## class 3: 0.9293 0.0707
## class 4: 0.9321 0.0679
##
## $a1g9communty
## Pr(1) Pr(2)
## class 1: 0.3012 0.6988
## class 2: 0.9916 0.0084
## class 3: 0.8553 0.1447
## class 4: 0.8209 0.1791
##
## $a1g9blocksch
## Pr(1) Pr(2)
## class 1: 0.0587 0.9413
## class 2: 0.0000 1.0000
## class 3: 0.1596 0.8404
## class 4: 0.1883 0.8117
##
## $a1g9double
## Pr(1) Pr(2)
## class 1: 0.2178 0.7822
## class 2: 0.0485 0.9515
## class 3: 0.5421 0.4579
## class 4: 0.5682 0.4318
##
## $a1g9study
## Pr(1) Pr(2)
## class 1: 0.3877 0.6123
## class 2: 0.9585 0.0415
## class 3: 0.6175 0.3825
## class 4: 0.6803 0.3197
##
## $a1g9teacher
## Pr(1) Pr(2)
## class 1: 0.1286 0.8714
## class 2: 0.9995 0.0005
## class 3: 0.6235 0.3765
## class 4: 0.7897 0.2103
##
## Estimated class population shares
## 0.206 0.1507 0.3812 0.2621
##
## Predicted class memberships (by modal posterior prob.)
## 0.1901 0.1544 0.3603 0.2952
##
## =========================================================
## Fit for 4 latent classes:
## =========================================================
## 2 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.11687 0.09417 1.241 0.215
## x1sexMale -0.01375 0.05199 -0.264 0.792
## x1black 0.18737 0.07543 2.484 0.013
## x1white -0.07310 0.06691 -1.093 0.275
## x1hispanic -0.16485 0.07027 -2.346 0.019
## x1localeRural 0.53988 0.07698 7.013 0.000
## x1localeSuburb -0.30381 0.06481 -4.688 0.000
## x1localeTown 0.09506 0.11126 0.854 0.393
## x1regionNortheast 0.47197 0.10192 4.631 0.000
## x1regionSouth -0.67357 0.06849 -9.835 0.000
## x1regionWest -0.76684 0.08770 -8.744 0.000
## =========================================================
## 3 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.62922 0.09620 6.540 0.000
## x1sexMale -0.04634 0.05020 -0.923 0.356
## x1black -0.24638 0.07777 -3.168 0.002
## x1white 0.26694 0.06655 4.011 0.000
## x1hispanic -0.16612 0.06670 -2.491 0.013
## x1localeRural 0.50370 0.07715 6.529 0.000
## x1localeSuburb -0.20002 0.06291 -3.179 0.001
## x1localeTown 0.83954 0.10009 8.388 0.000
## x1regionNortheast 0.78864 0.10201 7.731 0.000
## x1regionSouth -0.52601 0.06798 -7.737 0.000
## x1regionWest -0.40606 0.08336 -4.871 0.000
## =========================================================
## 4 / 1
## Coefficient Std. error t value Pr(>|t|)
## (Intercept) 0.51934 0.08760 5.929 0.000
## x1sexMale -0.00341 0.04764 -0.072 0.943
## x1black -0.30175 0.07491 -4.028 0.000
## x1white 0.39111 0.06366 6.144 0.000
## x1hispanic -0.36457 0.06541 -5.574 0.000
## x1localeRural 0.83217 0.07159 11.624 0.000
## x1localeSuburb -0.43264 0.05991 -7.222 0.000
## x1localeTown 0.72834 0.09614 7.576 0.000
## x1regionNortheast 0.41230 0.09639 4.277 0.000
## x1regionSouth -1.31308 0.06525 -20.123 0.000
## x1regionWest -0.38213 0.07310 -5.228 0.000
## =========================================================
## number of observations: 22046
## number of estimated parameters: 77
## residual degrees of freedom: 1970
## maximum log-likelihood: -119605.3
##
## AIC(4): 239364.5
## BIC(4): 239980.6
## X^2(4): 34789.35 (Chi-square goodness of fit)
##
## ALERT: estimation algorithm automatically restarted with new initial values
## probs.start <- LCA4$probs.start
plot(LCA4)
Brief Interpretation
Limitations and Next Step Analysis
Concluding Remarks
Reference
Ingels, S. J., Pratt, D. J., Herget, D. R., Burns, L. J., Dever, J. A.,
Ottem, R., Rogers, J. E., Jin, Y., & Leinwand, S. (2011). High
school longitudinal study of 2009 (HSLS: 09): Base-year data file
documentation. NCES 2011-328. National Center for Education
Statistics.
Kurban, E. R., & Cabrera, A. F. (2020). Building readiness and
intention towards STEM fields of study: Using HSLS: 09 and SEM to
examine this complex process among high school students. The Journal
of Higher Education, 91(4), 620–650.