cross-sectional lca
DESCRIPTION
Cross-sectional LCA. Patterns of first response to cigarettes. First smoking experience. Have you ever tried a cigarette (including roll-ups), even a puff? How old were you when you first tried a cigarette? - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/1.jpg)
Cross-sectional LCA
Patterns of first response to cigarettes
![Page 2: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/2.jpg)
First smoking experience
• Have you ever tried a cigarette (including roll-ups), even a puff?
• How old were you when you first tried a cigarette?
• When you FIRST ever tried a cigarette can you remember how it made you feel? (tick as many as you want)– It made me cough
– I felt ill
– It tasted awful
– I liked it
– It made me feel dizzy
![Page 3: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/3.jpg)
Aim
• To categorise the subjects based on their pattern of responses
• To assess the relationship between first-response and current smoking behaviour
• To try not to think too much about the possibility of recall bias
![Page 4: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/4.jpg)
Step 1
Look at your data!!!
![Page 5: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/5.jpg)
Examine your data structure
• LCA converts a large number of response patterns into a small number of ‘homogeneous’ groups
• If the responses in your data are fair mutually exclusive then there’s no point doing LCA
• Don’t just dive in
![Page 6: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/6.jpg)
How many items endorsed?
numresp | Freq. Percent Cum.------------+----------------------------------- 0 | 69 2.75 2.75 1 | 1,597 63.70 66.45 2 | 569 22.70 89.15 3 | 202 8.06 97.21 4 | 68 2.71 99.92 5 | 2 0.08 100.00------------+----------------------------------- Total | 2,507 100.00
![Page 7: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/7.jpg)
Frequency of each item (n ~ 2500)
0
200
400
600
800
1,000
1,200
1,400
cough ill taste liked dizzy
Num
ber
of p
ositi
ve r
espo
nses
![Page 8: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/8.jpg)
Examine pattern frequency
+---------------------------------------+
| cough ill taste liked dizzy num |
|---------------------------------------|
1. | 0 0 1 0 0 468 |
2. | 0 0 0 1 0 452 |
3. | 1 0 0 0 0 449 |
4. | 1 0 1 0 0 279 |
5. | 0 0 0 0 1 194 |
|---------------------------------------|
6. | 1 1 1 0 0 94 |
7. | 1 0 0 1 0 87 |
8. | 1 0 0 0 1 76 |
9. | 0 0 0 0 0 69 |
10. | 1 1 1 0 1 59 |
|---------------------------------------|
11. | 0 0 0 1 1 56 |
12. | 1 0 1 0 1 47 |
13. | 1 0 0 1 1 35 |
14. | 0 1 0 0 0 34 |
15. | 0 0 1 0 1 27 |
|---------------------------------------|
+---------------------------------------+
| cough ill taste liked dizzy num |
|---------------------------------------|
16. | 0 1 1 0 0 17 |
17. | 0 0 1 1 0 13 |
18. | 1 1 0 0 1 9 |
19. | 1 1 0 0 0 8 |
20. | 0 1 1 0 1 7 |
|---------------------------------------|
21. | 1 0 1 1 1 7 |
22. | 1 0 1 1 0 6 |
23. | 0 1 0 0 1 5 |
24. | 1 1 1 1 1 2 |
25. | 0 1 0 1 1 2 |
|---------------------------------------|
26. | 0 1 0 1 0 1 |
27. | 1 1 1 1 0 1 |
28. | 1 1 0 1 1 1 |
29. | 0 0 1 1 1 1 |
30. | 1 1 0 1 0 1 |
+---------------------------------------+
![Page 9: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/9.jpg)
Examine correlation structure
Polychoric correlation matrix
cough ill taste liked dizzy
cough 1
ill 0.371 1
taste 0.049 0.468 1
liked -0.510 -0.542 -0.786 1
dizzy -0.030 0.246 -0.241 -0.158 1
![Page 10: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/10.jpg)
Step 2
Now you can fit a latent class model
![Page 11: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/11.jpg)
Latent Class models
• Work with observations at the pattern level rather than the individual (person) level
+---------------------------------------+
| cough ill taste liked dizzy num |
|---------------------------------------|
1. | 0 0 1 0 0 468 |
2. | 0 0 0 1 0 452 |
3. | 1 0 0 0 0 449 |
4. | 1 0 1 0 0 279 |
5. | 0 0 0 0 1 194 |
|---------------------------------------|
![Page 12: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/12.jpg)
Latent Class models
• For a given number of latent classes, using application of Bayes’ rule plus an assumption of conditional independence one can calculate the probability that each pattern should fall into each class
• Derive the likelihood of the obtained data under each model (i.e. assuming different numbers of classes) and use this plus other fit statistics to determine optimal model i.e. optimal number of classes
![Page 13: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/13.jpg)
Latent Class models
• Bayes’ rule:
• Conditional independence: P( pattern = ’01’ | class = i)
= P(pat(1) = ‘0’ | class = i)*P(pat(2) = ‘1’ | class = i)
![Page 14: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/14.jpg)
How many classes can I have?~ degrees of freedom
• 32 possible patterns
• Each additional class requires – 5 df to estimate the 5 prevalence of each item that class
(i.e. 5 thresholds)
– 1 df for an additional cut of the latent variable defining the class distribution
• Hence a 5-class model uses up 5*5 + 4 = 29 degrees of freedom leaving 3df to test the model
![Page 15: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/15.jpg)
Standard thresholds
• Mplus thinks of binary variables as being a dichotomised continuous latent variable
• The point at which a continuous N(0,1) variable must be cut to create a binary variable is called a threshold
• A binary variable with 50% cases corresponds to a threshold of zero
• A binary variable with 2.5% cases corresponds to a threshold of 1.96
![Page 16: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/16.jpg)
Standard thresholds
Figure from Uebersax webpage
![Page 17: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/17.jpg)
Data: File is “..\smoking_experience.dta.dat"; listwise is on; Variable: Names are sex cough ill taste liked dizzy
numresp less_12 less_13;
categorical are cough ill taste liked dizzy ; usevariables are cough ill taste liked dizzy; Missing are all (-9999) ;
classes = c(3); Analysis: proc = 2 (starts); type = mixture; starts = 1000 500; stiterations = 20; Output: tech10;
![Page 18: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/18.jpg)
What you’re actually doing
model: %OVERALL%
[c#1 c#2];
%c#1% [cough$1]; [ill$1]; [taste$1]; [liked$1]; [dizzy$1];
+ five more threshold parameters for %c#2% and %c#3%
Defines the latent class variable
Defines the within class thresholds i.e. the prevalence of the endorsement of each item
![Page 19: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/19.jpg)
SUMMARY OF CATEGORICAL DATA PROPORTIONS
COUGH Category 1 0.537 Category 2 0.463 ILL Category 1 0.904 Category 2 0.096 TASTE Category 1 0.590 Category 2 0.410 LIKED Category 1 0.735 Category 2 0.265 DIZZY Category 1 0.789 Category 2 0.211
![Page 20: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/20.jpg)
RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES
Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers:
-6343.937 685561 9973 -6343.937 172907 9395 -6343.937 497824 9464 -6343.937 770684 7725 -6343.937 584663 5193 -6343.937 872295 2899 -6343.937 116150 3570 -6343.937 271339 4768 -6343.937 472383 9650 -6343.937 707126 3683Etc.
![Page 21: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/21.jpg)
How many random starts?
• Depends on– Sample size
– Complexity of model • Number of manifest variables
• Number of classes
• Aim to find consistently the model with the lowest likelihood, within each run
![Page 22: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/22.jpg)
Success Not there yetLoglikelihood values at local maxima,
seeds, and initial stage start numbers:
-10148.718 987174 1689 -10148.718 777300 2522 -10148.718 406118 3827 -10148.718 51296 3485 -10148.718 997836 1208 -10148.718 119680 4434 -10148.718 338892 1432 -10148.718 765744 4617 -10148.718 636396 168 -10148.718 189568 3651 -10148.718 469158 1145 -10148.718 90078 4008 -10148.718 373592 4396 -10148.718 73484 4058 -10148.718 154192 3972 -10148.718 203018 3813 -10148.718 785278 1603 -10148.718 235356 2878 -10148.718 681680 3557 -10148.718 92764 2064
Loglikelihood values at local maxima, seeds, and initial stage start numbers
-10153.627 23688 4596 -10153.678 150818 1050 -10154.388 584226 4481 -10155.122 735928 916 -10155.373 309852 2802 -10155.437 925994 1386 -10155.482 370560 3292 -10155.482 662718 460 -10155.630 320864 2078 -10155.833 873488 2965 -10156.017 212934 568 -10156.231 98352 3636 -10156.339 12814 4104 -10156.497 557806 4321 -10156.644 134830 780 -10156.741 80226 3041 -10156.793 276392 2927 -10156.819 304762 4712 -10156.950 468300 4176 -10157.011 83306 2432
![Page 23: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/23.jpg)
Scary “warnings”
IN THE OPTIMIZATION, ONE OR MORE LOGIT THRESHOLDS APPROACHED AND WERE SET AT THE EXTREME VALUES. EXTREME VALUES ARE -15.000 AND 15.000.
THE FOLLOWING THRESHOLDS WERE SET AT THESE VALUES:
* THRESHOLD 1 OF CLASS INDICATOR TASTE FOR CLASS 3 AT ITERATION 11* THRESHOLD 1 OF CLASS INDICATOR DIZZY FOR CLASS 3 AT ITERATION 12* THRESHOLD 1 OF CLASS INDICATOR ILL FOR CLASS 3 AT ITERATION 16* THRESHOLD 1 OF CLASS INDICATOR LIKED FOR CLASS 1 AT ITERATION 34* THRESHOLD 1 OF CLASS INDICATOR TASTE FOR CLASS 1 AT ITERATION 93
WARNING: WHEN ESTIMATING A MODEL WITH MORE THAN TWO CLASSES, IT MAY BE NECESSARY TO INCREASE THE NUMBER OF RANDOM STARTS USING THE STARTS OPTION TO AVOID LOCAL MAXIMA.
![Page 24: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/24.jpg)
THE MODEL ESTIMATION TERMINATED NORMALLY
TESTS OF MODEL FIT
Loglikelihood H0 Value -6343.937 H0 Scaling Correction Factor 1.006 for MLR
Information Criteria Number of Free Parameters 17 Akaike (AIC) 12721.873 Bayesian (BIC) 12820.930 Sample-Size Adjusted BIC 12766.916 (n* = (n + 2) / 24)
![Page 25: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/25.jpg)
Chi-Square Test of Model Fit for the Binary and Ordered Categorical (Ordinal) Outcomes
Pearson Chi-Square
Value 623.040
Degrees of Freedom 14
P-Value 0.0000
Likelihood Ratio Chi-Square
Value 563.869
Degrees of Freedom 14
P-Value 0.0000
![Page 26: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/26.jpg)
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL
Latent Classes 1 600.41143 0.23949 2 1517.83320 0.60544 3 388.75538 0.15507
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Latent Classes 1 630 0.25130 2 1396 0.55684 3 481 0.19186
![Page 27: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/27.jpg)
Entropy (fuzzyness)
CLASSIFICATION QUALITY
Entropy 0.832
Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column)
1 2 3 1 0.952 0.048 0.000 2 0.000 0.979 0.021 3 0.000 0.252 0.748
![Page 28: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/28.jpg)
Model results
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Latent Class 1
Thresholds
COUGH$1 1.604 0.133 12.103 0.000
ILL$1 7.371 4.945 1.490 0.136
TASTE$1 15.000 0.000 999.000 999.000
LIKED$1 -15.000 0.000 999.000 999.000
DIZZY$1 1.890 0.139 13.604 0.000
![Page 29: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/29.jpg)
Categorical Latent Variables
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Means
C#1 0.435 0.124 3.500 0.000
C#2 1.362 0.135 10.058 0.000
![Page 30: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/30.jpg)
RESULTS IN PROBABILITY SCALE
Latent Class 1
COUGH Category 1 0.833 0.018 45.072 0.000 Category 2 0.167 0.018 9.059 0.000 ILL Category 1 0.999 0.003 321.448 0.000 Category 2 0.001 0.003 0.202 0.840 TASTE Category 1 1.000 0.000 0.000 1.000 Category 2 0.000 0.000 0.000 1.000 LIKED Category 1 0.000 0.000 0.000 1.000 Category 2 1.000 0.000 0.000 1.000 DIZZY Category 1 0.869 0.016 54.848 0.000 Category 2 0.131 0.016 8.284 0.000
![Page 31: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/31.jpg)
Class 1 from 3-class model
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY
![Page 32: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/32.jpg)
Conditional independence
• The latent class variable accounts for the covariance structure in your dataset
• Conditional on C, any pair of manifest variables should be uncorrelated
• Harder to achieve for a cross-sectional LCA• With a longitudinal LCA there tends to be a more
ordered pattern of correlations based on proximity in time
![Page 33: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/33.jpg)
Tech10 – response patterns
MODEL FIT INFORMATION FOR THE LATENT CLASS INDICATOR MODEL PART
RESPONSE PATTERNS
No. Pattern No. Pattern No. Pattern No. Pattern 1 10000 2 00100 3 00010 4 11100 5 11101 6 00001 7 10101 8 10010 9 10100 10 00101 11 10001 12 0000013 00011 14 01101 15 10011 16 0011017 11000 18 10111 19 11011 20 0110021 10110 22 01000 23 01001 24 1111125 01010 26 11001 27 01011 28 1101029 00111 30 11110
![Page 34: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/34.jpg)
Tech10 – Bivariate model fit
• 5 manifest variables → number of pairs =
Overall Bivariate Pearson Chi-Square 215.353
Overall Bivariate Log-Likelihood Chi-Square 214.695
Compare with χ² (10 df) = 18.307
102
45
)!2()!3(
!5
2
5
![Page 35: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/35.jpg)
Tech10 – Bivariate model fit
Not bad:-
Estimated Probabilities Standardized Variable Variable H1 H0 Residual (z-score) COUGH ILL Category 1 Category 1 0.511 0.506 0.457 Category 1 Category 2 0.026 0.031 -1.321 Category 2 Category 1 0.393 0.398 -0.467 Category 2 Category 2 0.070 0.065 0.925
Bivariate Pearson Chi-Square 2.726 Bivariate Log-Likelihood Chi-Square 2.798
![Page 36: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/36.jpg)
Tech10 – Bivariate model fit
Terrible:-
Estimated Probabilities Standardized Variable Variable H1 H0 Residual (z-score) COUGH ILL Category 1 Category 1 0.566 0.534 3.149 Category 1 Category 2 0.338 0.370 -3.255 Category 2 Category 1 0.024 0.056 -6.850 Category 2 Category 2 0.072 0.040 7.977
Bivariate Pearson Chi-Square 116.657 Bivariate Log-Likelihood Chi-Square 117.162
![Page 37: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/37.jpg)
Conditional Independence violated
Need more classes
![Page 38: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/38.jpg)
Obtain the ‘optimal’ model
Assess the following for models with increasing classes• aBIC• Entropy• BLRT (Bootstrap LRT)• Conditional Independence (Tech10)
• Ease of interpretation• Consistency with previous work / theory
![Page 39: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/39.jpg)
Model fit stats
1 class 2 class 3 class 4 class 5 class
Estimated params 5 11 17 23 29
H0 Likelihood -6962.1 -6458.7 -6343.9 -6200.1 -6100.8
aBIC 13947.4 12968.5 12766.9 12507.1 12336.5
Entropy - 0.944 0.832 0.894 0.844
Tech 10 625.2 228.1 214.7 135.9 17.6
BLRT statistic - 1006.8 229.5 287.8 198.4
BLRT p-value - < 0.0001 < 0.0001 < 0.0001 < 0.0001
![Page 40: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/40.jpg)
5-class model
• aBIC values are still decreasing• Tech 10 is still quite high – residual correlations
between ill and both liked and dizzy
• BLRT rejects 4-class model• Not enough df to fit 6-class model so we cannot
assess fit of 5-class• Seems unlikely as BLRT values are decreasing
slowly
![Page 41: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/41.jpg)
Cross-sectional LCA
Patterns of first response to cigarette
Attempt 2
![Page 42: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/42.jpg)
What to do?
• We need more degrees of freedom• There were only 5 questions on response to smoking
• Add something else:– How old were you when you first tried a cigarette?
– Split into pre-teen / teen
• 6 binary variables means 64 d.f. to play with
![Page 43: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/43.jpg)
Model fit stats – attempt 2
3 class 4 class 5 class 6 class 7 class
Estimated params 20 27 34 41 48
H0 Likelihood -7866.3 -7720.2 -7616.0 -7582.4 -7576.2
aBIC 15825.6 15565.7 15389.9 15355.1 15375.2
Entropy 0.823 0.893 0.812 0.876 0.850
Tech 10 228.9 144.6 16.8 1.2 0.29
BLRT statistic 123.3 146.1 104.2 67.3 12.4
BLRT p-value < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.2100
![Page 44: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/44.jpg)
Model fit stats – attempt 2
3 class 4 class 5 class 6 class 7 class
Estimated params 20 27 34 41 48
H0 Likelihood -7866.3 -7720.2 -7616.0 -7582.4 -7576.2
aBIC 15825.6 15565.7 15389.9 15355.1 15375.2
Entropy 0.823 0.893 0.812 0.876 0.850
Tech 10 228.9 144.6 16.8 1.2 0.29
BLRT statistic 123.3 146.1 104.2 67.3 12.4
BLRT p-value < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.2100
![Page 45: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/45.jpg)
6-class model results
CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASSES BASED ON THE ESTIMATED MODEL
Latent classes
1 53.23894 2.1%
2 541.96140 21.7%
3 396.04196 15.9%
4 454.89294 18.2%
5 750.87470 30.1%
6 295.99007 11.9%
CLASSIFICATION OF INDIVIDUALS BASED ON THEIR MOST LIKELY LATENT CLASS MEMBERSHIP
Latent classes
1 34 1.4%
2 540 21.7%
3 403 16.2%
4 447 17.9%
5 840 33.7%
6 229 9.2%
![Page 46: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/46.jpg)
Examine entropy in more detail
• Model-level entropy = 0.876
• Class level entropy:
1 2 3 4 5 6 1 0.953 0.000 0.000 0.000 0.026 0.020 2 0.000 0.997 0.000 0.000 0.002 0.001 3 0.000 0.000 0.958 0.000 0.017 0.025 4 0.000 0.000 0.000 0.949 0.041 0.011 5 0.025 0.005 0.000 0.036 0.851 0.083 6 0.000 0.000 0.043 0.003 0.036 0.918
![Page 47: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/47.jpg)
Pattern level entropy
• Save out the model-based probabilities• Open in another stats package• Collapse over response patterns
![Page 48: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/48.jpg)
Save out the model-based probabilities
savedata:
file is "6-class-results.dat";
save cprobabilities;
![Page 49: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/49.jpg)
Varnames shown at end of output
SAVEDATA INFORMATION
Order and format of variables
COUGH F10.3 ILL F10.3 TASTE F10.3 LIKED F10.3 DIZZY F10.3 LESS_13 F10.3 ALN F10.3 QLET F10.3 SEX F10.3 CPROB1 F10.3 CPROB2 F10.3 CPROB3 F10.3 CPROB4 F10.3 CPROB5 F10.3 CPROB6 F10.3 C F10.3
![Page 50: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/50.jpg)
Open / process in Stata
Remove excess spaces from data file, then:
insheet using 6-class-results.dat, delim(" ")
local i = 1local varnames "COUGH ILL TASTE LIKED DIZZY LESS_13 ALN
QLET SEX CPROB1 CPROB2 CPROB3 CPROB4 CPROB5 CPROB6 C"
foreach x of local varnames {rename v`i' `x'local i=`i'+1}
gen num = 1collapse (mean) CPROB* C (count) num, by(COUGH ILL
TASTE LIKED DIZZY LESS_13)
![Page 51: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/51.jpg)
Check the assignment probabilities for each class
cough ill taste liked dizzy < 13 P_c1 P_c2 P_c3 P_c4 P_c5 P_c6Modclass n
1 1 1 0 0 0 0 0 0 0 0.052 0.948 6 64
1 1 1 0 1 0 0 0 0.003 0 0.001 0.996 6 34
1 1 1 0 0 1 0 0 0 0 0.027 0.973 6 30
1 0 1 0 1 0 0 0 0.135 0 0.062 0.803 6 29
1 1 1 0 1 1 0 0 0.003 0 0.001 0.996 6 25
1 0 1 0 1 1 0 0 0.154 0 0.032 0.815 6 18
1 1 0 0 0 0 0 0 0 0.071 0.054 0.874 6 6
0 1 1 0 1 1 0 0 0.073 0 0.012 0.915 6 4
1 1 0 0 1 0 0 0 0.303 0 0.001 0.696 6 4
1 1 0 0 1 1 0 0 0.329 0 0 0.671 6 4
0 1 1 0 0 1 0 0 0 0 0.411 0.589 6 3
0 1 1 0 1 0 0 0 0.065 0 0.024 0.912 6 3
1 1 0 0 0 1 0 0 0 0.055 0.029 0.917 6 2
1 1 1 1 0 1 0 0.001 0 0 0.023 0.977 6 1
1 1 1 1 1 0 0 0 0.039 0 0.001 0.96 6 1
1 1 1 1 1 1 0 0 0.044 0 0 0.955 6 1
![Page 52: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/52.jpg)
cough ill taste liked dizzy < 13 P_c1 P_c2 P_c3 P_c4 P_c5 P_c6Modclass n
1 1 1 0 0 0 0 0 0 0 0.052 0.948 6 64
1 1 1 0 1 0 0 0 0.003 0 0.001 0.996 6 34
1 1 1 0 0 1 0 0 0 0 0.027 0.973 6 30
1 0 1 0 1 0 0 0 0.135 0 0.062 0.803 6 29
1 1 1 0 1 1 0 0 0.003 0 0.001 0.996 6 25
1 0 1 0 1 1 0 0 0.154 0 0.032 0.815 6 18
1 1 0 0 0 0 0 0 0 0.071 0.054 0.874 6 6
0 1 1 0 1 1 0 0 0.073 0 0.012 0.915 6 4
1 1 0 0 1 0 0 0 0.303 0 0.001 0.696 6 4
1 1 0 0 1 1 0 0 0.329 0 0 0.671 6 4
0 1 1 0 0 1 0 0 0 0 0.411 0.589 6 3
0 1 1 0 1 0 0 0 0.065 0 0.024 0.912 6 3
1 1 0 0 0 1 0 0 0 0.055 0.029 0.917 6 2
1 1 1 1 0 1 0 0.001 0 0 0.023 0.977 6 1
1 1 1 1 1 0 0 0 0.039 0 0.001 0.96 6 1
1 1 1 1 1 1 0 0 0.044 0 0 0.955 6 1
Check the assignment probabilities for each class
![Page 53: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/53.jpg)
cough ill taste liked dizzy < 13 P_c1 P_c2 P_c3 P_c4 P_c5 P_c6Modclass n
1 1 1 0 0 0 0 0 0 0 0.052 0.948 6 64
1 1 1 0 1 0 0 0 0.003 0 0.001 0.996 6 34
1 1 1 0 0 1 0 0 0 0 0.027 0.973 6 30
1 0 1 0 1 0 0 0 0.135 0 0.062 0.803 6 29
1 1 1 0 1 1 0 0 0.003 0 0.001 0.996 6 25
1 0 1 0 1 1 0 0 0.154 0 0.032 0.815 6 18
1 1 0 0 0 0 0 0 0 0.071 0.054 0.874 6 6
0 1 1 0 1 1 0 0 0.073 0 0.012 0.915 6 4
1 1 0 0 1 0 0 0 0.303 0 0.001 0.696 6 4
1 1 0 0 1 1 0 0 0.329 0 0 0.671 6 4
0 1 1 0 0 1 0 0 0 0 0.411 0.589 6 3
0 1 1 0 1 0 0 0 0.065 0 0.024 0.912 6 3
1 1 0 0 0 1 0 0 0 0.055 0.029 0.917 6 2
1 1 1 1 0 1 0 0.001 0 0 0.023 0.977 6 1
1 1 1 1 1 0 0 0 0.039 0 0.001 0.96 6 1
1 1 1 1 1 1 0 0 0.044 0 0 0.955 6 1
Check the assignment probabilities for each class
![Page 54: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/54.jpg)
Bad taste (30.1%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 55: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/55.jpg)
Positive experience (21.7%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 56: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/56.jpg)
Coughed (18.2%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 57: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/57.jpg)
Dizziness (15.9%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 58: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/58.jpg)
V negative experience (11.9%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 59: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/59.jpg)
Felt ill (2.1%)
0
0.2
0.4
0.6
0.8
1
COUGH ILL TASTE LIKED DIZZY LESS_13
![Page 60: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/60.jpg)
Well that was a complete waste of time!
• You might think that those resulting classes could have been derived just looking at the response patterns and making some arbitrary decisions e.g.– Group all of those who had >1 negative experience
– Keep separate each group who had 1 experience
• You would have ended up with a bunch of weird patterns with no clue of what to do with them
• Strange patterns likely to be measurement error?
• LCA incorporates ALL patterns and deals with uncertainty through the posterior probabilities
![Page 61: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/61.jpg)
Conclusions / warning
• Like EFA, LCA is an exploratory tool with the aim of summarising the variability in the dataset in a simple/interpretable way
• These results do not prove that there are 6 groups of young people in real life.
• LCA will find groupings in the data even if there is no reason to think such groups might exist. It’s just mathematics and it knows no better
![Page 62: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/62.jpg)
Remember, we are dealing with probabilities
Model-based “Modal assignment”
Ill 53.24 2.1% 34 1.4%
Positive 541.96 21.7% 540 21.7%
Dizzy 396.04 15.9% 403 16.2%
Coughed 454.89 18.2% 447 17.9%
Bad taste 750.87 30.1% 840 33.7%
V negative 295.99 11.9% 229 9.2%
• Working with modal assignment is easy – chuck each pattern into it’s most likely class and pretend everything is OK
– Equivalent to doing a single imputation for missing data – shudder!
• Unless entropy is V high, stick with the probabilities
![Page 63: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/63.jpg)
Covariates and outcomes
![Page 64: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/64.jpg)
Merging the classes with other data
• In the “olden days”, you could pass your ID variable through Mplus so when you saved your class probabilities you could merge this with other data.
• Now you can pass other data through Mplus as well – hurrah!
Variable:
<snip>
auxiliary are ID sex;
![Page 65: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/65.jpg)
Reshaping the dataset
• To account for the uncertainty in our class variable we will need to weight by the posterior probabilities obtained from Mplus
• Weighted model requires a reshaping of the dataset so that each respondent has n-rows (for an n-class model) rather than just 1
![Page 66: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/66.jpg)
Pre-shaped – first 20 kids
| ID sex dev_18 dev_42 pclass1 pclass2 pclass3 pclass4 pclass5 modclass ||--------------------------------------------------------------------------------------------------|| 30004 male 3 . .001 0 .803 0 .197 3 || 30008 male 2 1 .908 0 0 .007 .085 1 || 30010 male 2 2 .053 .001 .052 0 .894 5 || 30023 male 1 3 .115 0 .596 .001 .288 3 || 30031 male 3 4 0 0 .983 0 .016 3 ||--------------------------------------------------------------------------------------------------|| 30033 male 4 4 .392 0 .397 0 .211 3 || 30042 male 1 3 0 0 .983 0 .016 3 || 30050 male 3 2 0 0 .983 0 .016 3 || 30051 male 2 2 0 0 0 1 0 4 || 30057 male 1 3 .135 0 .002 0 .864 5 ||--------------------------------------------------------------------------------------------------|| 30058 male 1 4 0 0 .958 0 .041 3 || 30064 male 2 4 0 0 .983 0 .016 3 || 30068 male 4 3 .001 0 .803 0 .197 3 || 30070 male 3 4 0 0 .983 0 .016 3 || 30072 male 1 1 0 0 .983 0 .016 3 ||--------------------------------------------------------------------------------------------------|| 30075 male 3 3 0 0 .982 0 .018 3 || 30088 male 3 4 .03 .002 .889 .003 .076 3 || 30095 male 3 . 0 0 .983 0 .016 3 || 30098 male 3 . .068 .158 .173 .018 .583 5 || 30104 male 4 1 .008 0 .775 0 .217 3 |+--------------------------------------------------------------------------------------------------+
![Page 67: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/67.jpg)
Pre-shaped – first 20 kids
| ID sex dev_18 dev_42 pclass1 pclass2 pclass3 pclass4 pclass5 modclass ||--------------------------------------------------------------------------------------------------|| 30004 male 3 . .001 0 .803 0 .197 3 || 30008 male 2 1 .908 0 0 .007 .085 1 || 30010 male 2 2 .053 .001 .052 0 .894 5 || 30023 male 1 3 .115 0 .596 .001 .288 3 || 30031 male 3 4 0 0 .983 0 .016 3 ||--------------------------------------------------------------------------------------------------|| 30033 male 4 4 .392 0 .397 0 .211 3 || 30042 male 1 3 0 0 .983 0 .016 3 || 30050 male 3 2 0 0 .983 0 .016 3 || 30051 male 2 2 0 0 0 1 0 4 || 30057 male 1 3 .135 0 .002 0 .864 5 ||--------------------------------------------------------------------------------------------------|| 30058 male 1 4 0 0 .958 0 .041 3 || 30064 male 2 4 0 0 .983 0 .016 3 || 30068 male 4 3 .001 0 .803 0 .197 3 || 30070 male 3 4 0 0 .983 0 .016 3 || 30072 male 1 1 0 0 .983 0 .016 3 ||--------------------------------------------------------------------------------------------------|| 30075 male 3 3 0 0 .982 0 .018 3 || 30088 male 3 4 .03 .002 .889 .003 .076 3 || 30095 male 3 . 0 0 .983 0 .016 3 || 30098 male 3 . .068 .158 .173 .018 .583 5 || 30104 male 4 1 .008 0 .775 0 .217 3 |+--------------------------------------------------------------------------------------------------+
covariates Posterior probs Modal class
![Page 68: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/68.jpg)
The reshaping
. reshape long pclass, i(id) j(class)
(note: j = 1 2 3 4 5)
Data wide -> long--------------------------------------------------------
-Number of obs. 5584 -> 27920Number of variables 66 -> 63j variable (5 values) -> classxij variables: pclass1 pclass2 ... pclass5 -> pclass--------------------------------------------------------
-
![Page 69: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/69.jpg)
Re-shaped – first 3 kids +--------------------------------------------------+ | id sex dev_18 dev_42 pclass class | |--------------------------------------------------| 1. | 30004 male 3 . .001 1 | 2. | 30004 male 3 . 0 2 | 3. | 30004 male 3 . .803 3 | 4. | 30004 male 3 . 0 4 | 5. | 30004 male 3 . .197 5 | |--------------------------------------------------| 6. | 30008 male 2 1 .908 1 | 7. | 30008 male 2 1 0 2 | 8. | 30008 male 2 1 0 3 | 9. | 30008 male 2 1 .007 4 | 10. | 30008 male 2 1 .085 5 | |--------------------------------------------------| 11. | 30010 male 2 2 .053 1 | 12. | 30010 male 2 2 .001 2 | 13. | 30010 male 2 2 .052 3 | 14. | 30010 male 2 2 0 4 | 15. | 30010 male 2 2 .894 5 | +--------------------------------------------------+
First kid
Third kid
Second kid
Sum = 1Constant within child
![Page 70: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/70.jpg)
Similar with our data:. list id SEX CPROB class C in 1/12
+---------------------------------+ | id SEX CPROB class C | |---------------------------------| 1. | 30012 2 0 1 4 | 2. | 30012 2 0 2 4 | 3. | 30012 2 0 3 4 | 4. | 30012 2 .945 4 4 | 5. | 30012 2 .045 5 4 | 6. | 30012 2 .01 6 4 | |---------------------------------| 7. | 30024 2 0 1 5 | 8. | 30024 2 0 2 5 | 9. | 30024 2 0 3 5 | 10. | 30024 2 0 4 5 | 11. | 30024 2 .991 5 5 | 12. | 30024 2 .009 6 5 | |---------------------------------|
First respondent
Second respondent
![Page 71: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/71.jpg)
Simple crosstab
. tab class SEX , row nofreq
| SEX class | 1 2 | Total-----------+----------------------+---------- Ill | 40.87 59.13 | 100.00 Positive | 40.87 59.13 | 100.00 Dizzy | 40.87 59.13 | 100.00 Coughed | 40.87 59.13 | 100.00 Bad taste | 40.87 59.13 | 100.00 V negative | 40.87 59.13 | 100.00 -----------+----------------------+---------- Total | 40.87 59.13 | 100.00
• Oops!
![Page 72: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/72.jpg)
Simple crosstab – take 2
. tab class SEX [iw = CPROB], row nofreq
| SEX class | Male Female | Total-----------+-------------------+------- Ill | 52.9% 47.1% | 100% Positive | 32.9% 67.1% | 100% Dizzy | 43.2% 56.8% | 100% Coughed | 40.8% 59.2% | 100% Bad taste | 45.2% 54.8% | 100% V negative | 39.3% 60.7% | 100% -----------+-------------------+------- Total | 40.9% 59.1% | 100%
![Page 73: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/73.jpg)
Compare with modal class assignment
. tab C SEX if (class==1), row nofreq
| SEX C | Male Female |-----------+-----------------+ Ill | 50.0% 50.0% | Positive | 33.0% 67.0% | Dizzy | 43.4% 56.6% | Coughed | 40.7% 59.3% | Bad taste | 45.4% 54.6% | V negative | 37.6% 62.4% | -----------+-----------------+ Total | 40.9% 59.1% |
. tab class SEX [iw = CPROB], row nofreq
| SEX class | Male Female |-----------+-----------------+ Ill | 52.9% 47.1% | Positive | 32.9% 67.1% | Dizzy | 43.2% 56.8% | Coughed | 40.8% 59.2% | Bad taste | 45.2% 54.8% | V negative | 39.3% 60.7% | -----------+-----------------+ Total | 40.9% 59.1% |
![Page 74: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/74.jpg)
Multinomial logistic. xi: mlogit class i.SEX [iw = CPROB], rrr
Multinomial logistic regression Number of obs = 2493 LR chi2(5) = 24.52 Prob > chi2 = 0.0002Log likelihood = -4053.3746 Pseudo R2 = 0.0030------------------------------------------------------------------------------ class | RRR Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------Ill | _ISEX_2 | .7322787 .2081189 -1.10 0.273 .4195259 1.278186-------------+----------------------------------------------------------------Positive | _ISEX_2 | 1.677364 .1965463 4.41 0.000 1.333175 2.110413-------------+----------------------------------------------------------------Dizzy | _ISEX_2 | 1.082775 .1355213 0.64 0.525 .8472297 1.383807-------------+----------------------------------------------------------------Coughed | _ISEX_2 | 1.194885 .1437877 1.48 0.139 .9438344 1.512712-------------+----------------------------------------------------------------V negative | _ISEX_2 | 1.274734 .1782148 1.74 0.083 .9692081 1.676572------------------------------------------------------------------------------(class==Bad taste is the base outcome)
![Page 75: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/75.jpg)
Class predicts binary outcome
. Outcome = weekly smoker at age of 15
char class[omit] 5. xi: logistic sm1100 i.class [iw = CPROB]
Logistic regression Number of obs = 2493 LR chi2(5) = 229.03 Prob > chi2 = 0.0000Log likelihood = -1168.697 Pseudo R2 = 0.0892
------------------------------------------------------------------------------ sm1100 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- Ill | 2.132652 .9125838 1.77 0.077 .9218961 4.933531 Positive | 7.190203 1.231216 11.52 0.000 5.140265 10.05766 Dizzy | 7.899915 1.413907 11.55 0.000 5.562583 11.21937 Coughed | 3.686492 .6831946 7.04 0.000 2.563689 5.301041 V negative | 2.243034 .497619 3.64 0.000 1.452099 3.46478------------------------------------------------------------------------------
![Page 76: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/76.jpg)
Compare with modal class. Posterior probabilities------------------------------------------------------------------------------ sm1100 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- Ill | 2.132652 .9125838 1.77 0.077 .9218961 4.933531 Positive | 7.190203 1.231216 11.52 0.000 5.140265 10.05766 Dizzy | 7.899915 1.413907 11.55 0.000 5.562583 11.21937 Coughed | 3.686492 .6831946 7.04 0.000 2.563689 5.301041 V negative | 2.243034 .497619 3.64 0.000 1.452099 3.46478------------------------------------------------------------------------------
Modal assignment------------------------------------------------------------------------------ sm1100 | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- Ill | 2.560182 1.291868 1.86 0.062 .9522577 6.88315 Positive | 7.802047 1.313428 12.20 0.000 5.609367 10.85184 Dizzy | 8.3454 1.467249 12.07 0.000 5.912796 11.77881 Coughed | 4.224301 .7686958 7.92 0.000 2.957071 6.034592 V negative | 2.861537 .6548723 4.59 0.000 1.827254 4.481255------------------------------------------------------------------------------
![Page 77: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/77.jpg)
Conclusions
• Young people at 15yrs can report a variety of responses to their first cigarette
• Certain responses are associated with current regular smoking behaviour
• 15 year-old girls are more likely to retrospectively report a positive experience
• Recall bias is likely to play a part in these associations
![Page 78: Cross-sectional LCA](https://reader035.vdocument.in/reader035/viewer/2022062217/56815315550346895dc13954/html5/thumbnails/78.jpg)
Conclusions
• LCA is an exploratory tool which can be used to simplify a set of binary responses
• Extension to ordinal responses is straight-forward
• The use of ordinal data is an alternative way to boost degrees of freedom
• Resulting probabilities can be used model latent class variable as a risk factor or outcome
• A modal class variable should be used with caution