R Notebook

Latent Class Analysis

Latent class analysis (LCA) is a statistical technique used to find qualitatively separate subgroups within populations that typically share certain exterior characteristics. LCA is based on the idea that patterns of scores across survey questions, assessment markers, or scales might explain membership in previously undetected groups (or classes). In more technical terms, LCA is used to detect latent (or unobserved) heterogeneity in samples (Hagenaars & McCutcheon, 2002).

Choosing the Software

LCA can be done with both paid and free statistical packages, such as STATA (StataCorp LLC, 1985–2019), SAS (SAS Institute Inc., 2016), R (Venables & Smith, 2019), and Mplus (L. K. Muthén & Muthén, 1998–2017). Also, free paackages, such as LatentGold (Vermunt & Magidson, 2016) and poLCA for R, have been made just for doing LCA (Linzer & Lewis, 2011).

In this exercise we chose to use poLCA for the R language since it’s a free and versitile choice. Furthermore, it provides a wide set of data sample which can be used to learn the techinique.

Dataset Description

The chosen data is from the American National Election Study of 2000. This dataset is available as a sample of the poLCA library in R. You can find two sets of six questions, each with four possible replies, asked respondents to assess the degree to which Al Gore and George W. Bush exemplify certain characteristics (moral, compassionate, knowledgeable, excellent leader, dishonest, bright). The responses are (1) Very well; (2) Fairly well; (3) Not too well; and (4) Not at all well. Variable numbers of missing data exist for several responders on these factors.

The data set also has the possible factors VOTE3, which is the respondent’s 2000 vote choice (if asked), AGE, which is the respondent’s age, EDUC, which is the respondent’s level of education, GENDER, which is the respondent’s gender, and PARTY, which is the respondent’s Democratic-Republican political affiliation. Gore, Bush, and Other are the codes for VOTE3.

EDUC falls into the following categories: (1) 8 grades or less; (2) 9–11 grades, no further education; (3) High school diploma or equivalency; (4) More than 12 years of schooling, no higher degree; (5) Junior or community college level degree; (6) BA level degree, no further degree; (7) Advanced degree.

For GENDER, (1) Male and (2) Female are used to code male and female.

The PARTY variable is coded as follows: (1) Strong Democrat; (2) Weak Democrat; (3) Independent-Democrat; (4) Independent-Independent; (5) Independent-Republican; (6) Weak Republican; (7) Strong Republican.

Required Pakacge Install

install.packages("poLCA")
library("poLCA")

Saving the sample dataset into a new variable

data(election)

Warning in data(election) : data set ‘election’ not found

head(election)

Show a summary of the dataframe

summary(election)

               MORALG                  CARESG                  KNOWG                   LEADG                  DISHONG                  INTELG                  MORALB                  CARESB                  KNOWB    
 1 Extremely well :423   1 Extremely well :277   1 Extremely well :461   1 Extremely well :258   1 Extremely well :133   1 Extremely well :494   1 Extremely well :340   1 Extremely well :155   1 Extremely well :274  
 2 Quite well     :820   2 Quite well     :713   2 Quite well     :997   2 Quite well     :728   2 Quite well     :312   2 Quite well     :995   2 Quite well     :841   2 Quite well     :625   2 Quite well     :933  
 3 Not too well   :287   3 Not too well   :464   3 Not too well   :212   3 Not too well   :522   3 Not too well   :629   3 Not too well   :182   3 Not too well   :330   3 Not too well   :562   3 Not too well   :379  
 4 Not well at all:133   4 Not well at all:232   4 Not well at all: 59   4 Not well at all:185   4 Not well at all:557   4 Not well at all: 65   4 Not well at all: 98   4 Not well at all:342   4 Not well at all:133  
 NA's             :122   NA's             : 99   NA's             : 56   NA's             : 92   NA's             :154   NA's             : 49   NA's             :176   NA's             :101   NA's             : 66  
                                                                                                                                                                                                                        
                                                                                                                                                                                                                        
               LEADB                  DISHONB                  INTELB        VOTE3            AGE             EDUC           GENDER         PARTY      
 1 Extremely well :266   1 Extremely well : 70   1 Extremely well :329   Min.   :1.000   Min.   :18.00   Min.   :1.000   Min.   :1.00   Min.   :1.000  
 2 Quite well     :842   2 Quite well     :288   2 Quite well     :967   1st Qu.:1.000   1st Qu.:34.00   1st Qu.:3.000   1st Qu.:1.00   1st Qu.:2.000  
 3 Not too well   :407   3 Not too well   :653   3 Not too well   :306   Median :1.000   Median :45.00   Median :4.000   Median :2.00   Median :3.000  
 4 Not well at all:166   4 Not well at all:574   4 Not well at all:110   Mean   :1.534   Mean   :47.12   Mean   :4.305   Mean   :1.56   Mean   :3.726  
 NA's             :104   NA's             :200   NA's             : 73   3rd Qu.:2.000   3rd Qu.:58.00   3rd Qu.:6.000   3rd Qu.:2.00   3rd Qu.:6.000  
                                                                         Max.   :3.000   Max.   :97.00   Max.   :7.000   Max.   :2.00   Max.   :7.000  
                                                                         NA's   :625     NA's   :9       NA's   :6                      NA's   :25     

Create a latent class with loglinear indendence and 1~3 classes of data.

#create a latent class with loglinear indendence and 3 classes of data.
f = cbind(MORALG,CARESG,KNOWG,LEADG,DISHONG,INTELG,
MORALB,CARESB,KNOWB,LEADB,DISHONB,INTELB)~1
nes1 = poLCA(f,election,nclass=1) 

Conditional item response (column) probabilities,
 by outcome variable, for each class (row) 
 
$MORALG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.2578       0.4783         0.1808            0.0831

$CARESG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1594       0.4272         0.2807            0.1327

$KNOWG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.2723       0.5622         0.1297            0.0359

$LEADG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:             0.148       0.4249         0.3143            0.1129

$DISHONG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0877       0.1869         0.3898            0.3356

$INTELG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:             0.286       0.5667         0.1098            0.0374

$MORALB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:             0.209       0.5195         0.2136             0.058

$CARESB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0999       0.3791         0.3349            0.1861

$KNOWB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1594       0.5454         0.2174            0.0778

$LEADB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1632       0.5072         0.2426             0.087

$DISHONB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0427         0.18         0.4218            0.3555

$INTELB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1937       0.5545         0.1869            0.0648

Estimated class population shares 
 1 
 
Predicted class memberships (by modal posterior prob.) 
 1 
 
========================================================= 
Fit for 1 latent classes: 
========================================================= 
number of observations: 1311 
number of estimated parameters: 36 
residual degrees of freedom: 1275 
maximum log-likelihood: -18647.31 
 
AIC(1): 37366.62
BIC(1): 37553.05
G^2(1): 18882 (Likelihood ratio/deviance statistic) 
X^2(1): 29318840470 (Chi-square goodness of fit) 
 

nes2 = poLCA(f,election,nclass=2) 

Conditional item response (column) probabilities,
 by outcome variable, for each class (row) 
 
$MORALG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1172       0.4647         0.2806            0.1375
class 2:            0.4247       0.4944         0.0623            0.0186

$CARESG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0426       0.3407         0.4154            0.2014
class 2:            0.2982       0.5298         0.1208            0.0512

$KNOWG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1349       0.6121         0.2049            0.0481
class 2:            0.4354       0.5029         0.0404            0.0214

$LEADG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0375       0.3188         0.4596            0.1840
class 2:            0.2791       0.5508         0.1417            0.0284

$DISHONG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1321        0.287         0.3879             0.193
class 2:            0.0350        0.068         0.3921             0.505

$INTELG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1606       0.6271         0.1641            0.0481
class 2:            0.4349       0.4951         0.0454            0.0246

$MORALB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.3177       0.5809         0.0933            0.0081
class 2:            0.0799       0.4465         0.3564            0.1172

$CARESB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1724       0.5825         0.2216            0.0234
class 2:            0.0138       0.1376         0.4693            0.3793

$KNOWB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.2449       0.6786         0.0763            0.0002
class 2:            0.0579       0.3873         0.3849            0.1699

$LEADB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.2789       0.6532         0.0628            0.0050
class 2:            0.0259       0.3339         0.4560            0.1842

$DISHONB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0208       0.0961         0.3854            0.4977
class 2:            0.0688       0.2796         0.4650            0.1865

$INTELB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.2763       0.6686         0.0551            0.0000
class 2:            0.0958       0.4191         0.3433            0.1418

Estimated class population shares 
 0.5428 0.4572 
 
Predicted class memberships (by modal posterior prob.) 
 0.5454 0.4546 
 
========================================================= 
Fit for 2 latent classes: 
========================================================= 
number of observations: 1311 
number of estimated parameters: 73 
residual degrees of freedom: 1238 
maximum log-likelihood: -17344.92 
 
AIC(2): 34835.85
BIC(2): 35213.88
G^2(2): 16277.22 (Likelihood ratio/deviance statistic) 
X^2(2): 257217240886 (Chi-square goodness of fit) 
 

nes3 = poLCA(f,election,nclass=3) 

Conditional item response (column) probabilities,
 by outcome variable, for each class (row) 
 
$MORALG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.1013       0.5990         0.2552            0.0446
class 2:            0.1851       0.3668         0.2350            0.2131
class 3:            0.5224       0.4109         0.0390            0.0277

$CARESG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0227       0.5090         0.3819            0.0864
class 2:            0.0879       0.2546         0.3524            0.3051
class 3:            0.3970       0.4605         0.0895            0.0529

$KNOWG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0429       0.8058         0.1408            0.0105
class 2:            0.2542       0.4253         0.2382            0.0822
class 3:            0.5878       0.3543         0.0266            0.0312

$LEADG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0207       0.4886         0.4268            0.0639
class 2:            0.0747       0.2582         0.3856            0.2816
class 3:            0.3747       0.4772         0.1085            0.0396

$DISHONG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0519       0.2182         0.4998            0.2301
class 2:            0.2007       0.3060         0.2774            0.2158
class 3:            0.0426       0.0487         0.3371            0.5717

$INTELG
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0600       0.7953         0.1317            0.0130
class 2:            0.2936       0.4407         0.1852            0.0805
class 3:            0.5763       0.3698         0.0197            0.0341

$MORALB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0642       0.7137         0.2164            0.0057
class 2:            0.5797       0.3787         0.0248            0.0168
class 3:            0.0966       0.3795         0.3638            0.1601

$CARESB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0093       0.4847         0.4380            0.0679
class 2:            0.3483       0.5362         0.0836            0.0319
class 3:            0.0162       0.1125         0.4045            0.4668

$KNOWB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0191       0.7583         0.2182            0.0045
class 2:            0.4970       0.4899         0.0132            0.0000
class 3:            0.0682       0.3115         0.3828            0.2374

$LEADB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0537       0.7119         0.2217            0.0127
class 2:            0.5106       0.4648         0.0187            0.0058
class 3:            0.0236       0.2735         0.4524            0.2505

$DISHONB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0134       0.1471         0.5683            0.2711
class 2:            0.0365       0.0740         0.1993            0.6902
class 3:            0.0862       0.3096         0.4111            0.1931

$INTELB
          1 Extremely well 2 Quite well 3 Not too well 4 Not well at all
class 1:            0.0435       0.7741         0.1796            0.0028
class 2:            0.5284       0.4656         0.0060            0.0000
class 3:            0.1179       0.3391         0.3440            0.1990

Estimated class population shares 
 0.4194 0.2608 0.3198 
 
Predicted class memberships (by modal posterior prob.) 
 0.4256 0.2578 0.3166 
 
========================================================= 
Fit for 3 latent classes: 
========================================================= 
number of observations: 1311 
number of estimated parameters: 110 
residual degrees of freedom: 1201 
maximum log-likelihood: -16714.66 
 
AIC(3): 33649.32
BIC(3): 34218.96
G^2(3): 15016.7 (Likelihood ratio/deviance statistic) 
X^2(3): 16748681903 (Chi-square goodness of fit) 
 

Create a Three-class model with a single covariate (party)

f2a <- cbind(MORALG,CARESG,KNOWG,LEADG,DISHONG,INTELG,
MORALB,CARESB,KNOWB,LEADB,DISHONB,INTELB)~PARTY

nes2a <- poLCA(f2a,election,nclass=3,nrep=5) 
pidmat <- cbind(1,c(1:7))
exb <- exp(pidmat %*% nes2a$coeff)

Plotting the probability of candidate’s affinity class by ID

matplot(c(1:7),(cbind(1,exb)/(1+rowSums(exb))),ylim=c(0,1),type="l",
main="Party ID as a predictor of candidate affinity class",
xlab="Party ID: strong Democratic (1) to strong Republican (7)",
ylab="Probability of latent class membership",lwd=2,col=1)
text(5.9,0.35,"Other")

text(5.4,0.7,"Bush affinity")
text(1.8,0.6,"Gore affinity")