Social patterning in
bed-sharing behaviour
A longitudinal latent class analysis (LLCA)
Aim
• Examine proximal sleeping arrangements between
parents and their infant/child in terms of
– Potential influences on other care practices
– Perceived benefits to parents/child
• Effect of bed-sharing practices on
– Breastfeeding / pacifier use / infant well-being
– Child development / behaviour / health / sleeping patterns
– Maternal anxiety / bonding / sleep duration
Bed-sharing definition
• Not easy!
– Occupants of the bed / the room and proximity to parents
can change throughout the night / between different days of
week
• Bed-sharer – if they usually shared a bed with an
adult for nocturnal sleep (not nec. the parental bed)
• Bed-sharing took priority if a variety of practices
were reported either between days or across the
period of a single night
Rates of bed-sharing (n = 7447)
1750
1500
1250
1000
750
500
250
0
t1
t2
t3
t4
t5
C/S association – t1
S-class | Not bed-sh
Bed-sh |
Total
-----------+----------------------+---------Lo |
3,417
363 |
3,780
|
90.40
9.60 |
100.00
-----------+----------------------+---------Hi |
2,145
406 |
2,551
|
84.08
15.92 |
100.00
-----------+----------------------+---------Total |
5,562
769 |
6,331
|
87.85
12.15 |
100.00
Pearson chi2(1) =
56.8686
Pr = 0.000
C/S association – t2
S-class | Not bed-sh
Bed-sh |
Total
-----------+----------------------+---------Lo |
3,224
556 |
3,780
|
85.29
14.71 |
100.00
-----------+----------------------+---------Hi |
2,152
399 |
2,551
|
84.36
15.64 |
100.00
-----------+----------------------+---------Total |
5,376
955 |
6,331
|
84.92
15.08 |
100.00
Pearson chi2(1) =
1.0327
Pr = 0.310
C/S association – t3
S-class | Not bed-sh
Bed-sh |
Total
-----------+----------------------+---------Lo |
3,067
713 |
3,780
|
81.14
18.86 |
100.00
-----------+----------------------+---------Hi |
2,171
380 |
2,551
|
85.10
14.90 |
100.00
-----------+----------------------+---------Total |
5,238
1,093 |
6,331
|
82.74
17.26 |
100.00
Pearson chi2(1) =
16.7750
Pr = 0.000
C/S association – t4
S-class | Not bed-sh
Bed-sh |
Total
-----------+----------------------+---------Lo |
2,898
882 |
3,780
|
76.67
23.33 |
100.00
-----------+----------------------+---------Hi |
2,070
481 |
2,551
|
81.14
18.86 |
100.00
-----------+----------------------+---------Total |
4,968
1,363 |
6,331
|
78.47
21.53 |
100.00
Pearson chi2(1) =
18.0785
Pr = 0.000
C/S association – t5
S-class | Not bed-sh
Bed-sh |
Total
-----------+----------------------+---------Lo |
2,936
844 |
3,780
|
77.67
22.33 |
100.00
-----------+----------------------+---------Hi |
2,072
479 |
2,551
|
81.22
18.78 |
100.00
-----------+----------------------+---------Total |
5,008
1,323 |
6,331
|
79.10
20.90 |
100.00
Pearson chi2(1) =
11.6191
Pr = 0.001
Model fit stats
1 class
2 class
3 class
4 class
5 class
5
11
17
23
29
H0 Likelihood
-17113.2
-15276.9
-15116.3
-15027.6
-15024.4
aBIC
34255.1
30617.0
30330.2
30260.3
30215.2
Entropy
-
0.758
0.792
0.732
0.662
Tech 10
5438.9
343.7
24.3
0.18
0.05
BLRT statistic
-
3672.6
321.2
177.5
6.41
BLRT p-value
-
< 0.0001
< 0.0001
< 0.0001
0.4700
Estimated params
Note = aBIC still decreasing +
entropy never particularly high
Class sizes
FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT CLASS PATTERNS
BASED ON ESTIMATED POSTERIOR PROBABILITIES
Latent classes
1
2
3
4
1240.78344
969.53997
4761.71765
474.95894
0.16662
0.13019
0.63941
0.06378
CLASSIFICATION OF INDIVIDUALS BASED ON MOST LIKELY LATENT CLASS MEMBERSHIP
Latent classes
1
2
3
4
1218
650
5075
504
0.16356
0.08728
0.68148
0.06768
Entropy
CLASSIFICATION QUALITY
Entropy
0.732
Average Latent Class Probabilities for Most Likely Latent
Class Membership (Row) by Latent Class (Column)
1
1
2
3
4
0.814
0.048
0.029
0.145
2
0.031
0.850
0.067
0.074
3
0.122
0.042
0.904
0.000
4
0.033
0.060
0.000
0.781
Entropy
CLASSIFICATION QUALITY
Entropy
0.732
Not a weighted
average!!
Average Latent Class Probabilities for Most Likely Latent
Class Membership (Row) by Latent Class (Column)
1
1
2
3
4
0.814
0.048
0.029
0.145
2
0.031
0.850
0.067
0.074
3
0.122
0.042
0.904
0.000
4
0.033
0.060
0.000
0.781
Class 1 (16.7%)
+---------------------------------------------------------------------------+
| bed_t1 bed_t2 bed_t3 bed_t4 bed_t5
p_c1
p_c2
p_c3
p_c4
num |
|---------------------------------------------------------------------------|
|
0
0
0
0
0
.951
0
.04
.009
4150 |
|
0
0
0
0
1
.723
.001
.081
.194
348 |
|
1
0
0
0
0
.723
0
.266
.011
300 |
|
0
0
1
0
0
.649
.003
.221
.128
231 |
|
1
0
0
0
1
.406
.01
.401
.182
46 |
+---------------------------------------------------------------------------+
Class 2 (13.0%)
+---------------------------------------------------------------------------+
| bed_t1 bed_t2 bed_t3 bed_t4 bed_t5
p_c1
p_c2
p_c3
p_c4
num |
|---------------------------------------------------------------------------|
|
0
1
1
1
1
0
.836
.006
.158
141 |
|
1
1
1
1
1
0
.974
.004
.022
92 |
|
0
1
0
1
1
0
.541
.04
.418
64 |
|
0
1
1
1
0
0
.743
.074
.184
62 |
|
1
1
1
1
0
0
.916
.057
.027
42 |
|
1
1
0
1
1
0
.877
.041
.081
35 |
|
0
1
1
0
1
.001
.468
.381
.15
34 |
|
1
1
1
0
1
0
.644
.331
.025
18 |
|
1
1
0
1
0
.001
.559
.371
.068
16 |
+---------------------------------------------------------------------------+
Class 3 (63.9%)
+---------------------------------------------------------------------------+
| bed_t1 bed_t2 bed_t3 bed_t4 bed_t5
p_c1
p_c2
p_c3
p_c4
num |
|---------------------------------------------------------------------------|
|
0
1
0
0
0
.066
.007
.913
.013
255 |
|
1
1
0
0
0
.008
.013
.977
.003
118 |
|
0
1
1
0
0
.008
.077
.883
.032
82 |
|
0
1
0
0
1
.021
.089
.773
.117
49 |
|
0
1
0
1
0
.011
.323
.34
.326
49 |
|
1
1
1
0
0
.001
.121
.872
.006
42 |
|
1
0
1
0
0
.228
.013
.683
.075
32 |
|
1
1
0
0
1
.003
.151
.823
.024
23 |
+---------------------------------------------------------------------------+
Class 4 (6.4%)
+--------------------------------------------------------------------------+
| bed_t1 bed_t2 bed_t3 bed_t4 bed_t5
p_c1
p_c2
p_c3
p_c4
num |
|--------------------------------------------------------------------------|
|
0
0
0
1
1
.024
.011
.006
.959
324 |
|
0
0
0
1
0
.401
.005
.037
.557
296 |
|
0
0
1
1
1
.001
.045
.002
.952
263 |
|
0
0
1
1
0
.031
.033
.023
.913
139 |
|
0
0
1
0
1
.129
.02
.118
.733
75 |
|
1
0
0
1
1
.013
.084
.028
.875
30 |
|
1
0
1
1
1
.001
.278
.009
.712
29 |
|
1
0
0
1
0
.233
.039
.187
.541
28 |
|
1
0
1
1
0
.014
.206
.092
.689
24 |
|
1
0
1
0
1
.048
.105
.388
.459
10 |
+--------------------------------------------------------------------------+
4-class model ‘trajectories’
1
0.8
c4 (6.4%)
0.6
c1 (16.7%)
0.4
c2 (13.0%)
c3 (63.9%)
0.2
0
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
t5 (42mn)
Multinomial model
Multinomial logistic regression
Log likelihood =
-6450.991
Number of obs
LR chi2(3)
Prob > chi2
Pseudo R2
=
=
=
=
6331
22.31
0.0001
0.0017
-------------------------------------------------------------------------------class
|
RRR
Std. Err.
z
P>|z|
[95% Conf. Interval]
---------------+---------------------------------------------------------------Always Bed-sh |
Hi Soc Class |
.8664276
.0935659
-1.33
0.184
.7011495
1.070666
---------------+---------------------------------------------------------------Early Bed-sh
|
Hi Soc Class |
1.167799
.0895738
2.02
0.043
1.004797
1.357244
---------------+---------------------------------------------------------------Late Bed-sh
|
Hi Soc Class |
.767075
.0557954
-3.65
0.000
.6651556
.8846111
-------------------------------------------------------------------------------(class==Non Bed-share is the base outcome)
Latent Class Growth Analysis
T1
Risk
factors
T2
C
T3
T4
T5
Outcome
T1
T2
s
i
Risk
factors
T3
C
T4
T5
q
Outcome
Latent Class Growth Analysis
• Alternative to LLCA
• Fits polynomials on logit scale, not in probability
space (more flexible than one might think)
• Recall that LLCA items thresholds also estimated on
logit scale
• More parsimonius than LLCA (less parameters)
• Unlikely to capture some shapes e.g. a relapse
LCGA in Mplus
• Shorthand
i s q | y1@0 y2@1 y3@2 y4@3 y5@4;
• Longhand
i by y1@0 y2@0 y3@0 y4@0 y5@0;
s by y1@0 y2@1 y3@2 y4@3 y5@4;
q by y1@0 y2@2 y3@4 y4@9 y5@16;
[y1-y5@0 i s q];
• i/s/q are factors defined by FIXING loadings onto the manifest variables
• In LCGA these growth factors are constant (zero variance) and are
uncorrelated
• In GMM the growth factors have a variance, and are correlated with each
other (Cor(i,s) ne 0)
Choosing the growth parameters
• With LLCA there are no choices to be made
regarding how to describe/parameterize the
‘trajectories’ – they don’t really exist
• With LCGA you can fit:
–
–
–
–
–
4-class linear
4-class quadratic
4-class with two linear and two quadratic
4-class with 1 cubic, 1 quad, 1 linear, 1 constant
Etc.
Choosing the factor loadings
• We have five repeated measures
1, 6, 18, 30 and 42 months
Options:
i s q | bedt1@1 bedt2@6 bedt3@18 bedt4@30 bedt5@42
i s q | bedt1@0 bedt2@5 bedt3@17 bedt4@29 bedt5@41
i s q | bedt1@0.083 bedt2@0.5 bedt3@1.5 bedt4@2.5 bedt5@3.5
Effect of different choices (4 class)
i s q | beds_ka@1 beds_kb@6 beds_kd@18 beds_kf@30 beds_kj@42;
7266 perturbed starting value run(s) did not converge.
Final stage loglikelihood values at local maxima, seeds, and
initial stage start numbers:
-15077.633
377466
11367
ONE OR MORE MULTINOMIAL LOGIT PARAMETERS WERE FIXED TO AVOID
SINGULARITY OF THE INFORMATION MATRIX.
THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT
IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT
DISTRIBUTION OF THE CATEGORICAL LATENT VARIABLES AND ANY
INDEPENDENT VARIABLES.
THE FOLLOWING PARAMETERS WERE FIXED:
13 15
Effect of different choices (4 class)
i s q | beds_ka@0.083 beds_kb@0.5 beds_kd@1.5 beds_kf@2.5
beds_kj@3.5;
21 perturbed starting value run(s) did not converge.
Final stage loglikelihood values at local maxima, seeds, and
initial stage start numbers:
-15077.612
930654
1156
THE MODEL ESTIMATION TERMINATED NORMALLY
4-class MODEL RESULTS
Two-Tailed
P-Value
Estimate
S.E.
Est./S.E.
|
BEDS_t1
BEDS_t2
BEDS_t3
BEDS_t4
BEDS_t5
1.000
1.000
1.000
1.000
1.000
0.000
0.000
0.000
0.000
0.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
|
BEDS_t1
BEDS_t2
BEDS_t3
BEDS_t4
BEDS_t5
0.083
0.500
1.500
2.500
3.500
0.000
0.000
0.000
0.000
0.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
|
BEDS_t1
BEDS_t2
BEDS_t3
BEDS_t4
BEDS_t5
0.007
0.250
2.250
6.250
12.250
0.000
0.000
0.000
0.000
0.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
999.000
Latent Class 1
I
S
Q
All fixed
(not
estimated)
4-class MODEL RESULTS
Estimate
S.E.
Est./S.E.
Two-Tailed
P-Value
Latent Class 1
Means
I
S
Q
Thresholds
BEDS_t1$1
BEDS_t2$1
BEDS_t3$1
BEDS_t4$1
BEDS_t5$1
2.001
1.452
-0.311
0.144
0.146
0.037
13.876
9.975
-8.319
0.000
0.000
0.000
2.662
2.662
2.662
2.662
2.662
0.086
0.086
0.086
0.086
0.086
31.010
31.010
31.010
31.010
31.010
0.000
0.000
0.000
0.000
0.000
Estimated +
different
across
classes
Estimated
+ equal
across
classes
4-class LCGA model
1
0.8
c2 (8.0%)
0.6
c1 (15.4%)
0.4
c4 (72.9%)
c3 (3.7%)
0.2
0
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
t5 (42mn)
4-class LCGA model
1
0.8
c2 (8.0%)
0.6
c1 (15.4%)
0.4
c4 (72.9%)
c3 (3.7%)
0.2
0
t1 (1mn)
t2 (6mn)
These are all quadratics!
t3 (18mn)
t4 (30mn)
t5 (42mn)
Comparison with LLCA result
LCGA
LLCA
1
1
0.8
0.8
c2 (8.0%)
c4 (6.4%)
0.6
c1 (15.4%)
0.6
c1 (16.7%)
0.4
c4 (72.9%)
0.4
c2 (13.0%)
c3 (63.9%)
c3 (3.7%)
0.2
0.2
0
0
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
t5 (42mn)
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
Entropy = 0.805
Entropy = 0.732
aBIC = 30241.3
aBIC = 30260.3
t5 (42mn)
Comparison with LLCA result
LCGA
LLCA
1
1
0.8
0.8
c2 (8.0%)
c4 (6.4%)
0.6
c1 (15.4%)
0.6
c1 (16.7%)
0.4
c4 (72.9%)
0.4
c2 (13.0%)
c3 (63.9%)
c3 (3.7%)
0.2
0.2
0
0
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
t5 (42mn)
t1 (1mn)
t2 (6mn)
t3 (18mn)
t4 (30mn)
Entropy = 0.805
Entropy = 0.732
aBIC = 30241.3
aBIC = 30260.3
t5 (42mn)
Curves may look similar(ish), but check class distribution and
pattern assignment
Model fitting
• Aim is to find the simplest model which explains the
data
• As with LCA, compare models with different classes
• Simplify polynomials if possible
– Start with i/s/q and then constrain q terms to be zero if they
are negligible
How constraints can get you out of a pickle
• 5-class model:
ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE
INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE
MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT
DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL.
THE FOLLOWING PARAMETERS WERE FIXED:
10
Output: tech1;
PARAMETER SPECIFICATION FOR LATENT CLASS INDICATOR GROWTH MODEL PART
1
ALPHA(F) FOR LATENT CLASS 1
I
S
________
________
2
3
Q
________
4
1
ALPHA(F) FOR LATENT CLASS 2
I
S
________
________
5
6
Q
________
7
1
ALPHA(F) FOR LATENT CLASS 3
I
S
________
________
8
9
Q
________
10
Constrain a ‘q’ to be zero
%OVERALL%
i s q | beds_ka@0.083 beds_kb@0.5
beds_kd@1.5 beds_kf@2.5 beds_kj@3.5;
%c#1%
[q@0];
• Then re-run the model – doesn’t always work!!!
Conclusions
• LLCA / LCGA can be fitted to repeated binary data
• LCGA uses less parameters but cannot capture all
shapes so equivalent model may be more
parsimonious but have poorer fit
• Output from both is posterior probabilities for class
membership → weighted regression models