Social patterning in bedsharing behaviour

1
Social patterning in bed-sharing behaviour

• A longitudinal latent class analysis (LLCA)

2
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

3
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

4
Rates of bed-sharing (n 7447)
5
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

6
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

7
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

8
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

9
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

10
Model fit stats
Note aBIC still decreasing entropy never
particularly high
11
Class sizes

• FINAL CLASS COUNTS AND PROPORTIONS FOR THE LATENT
  CLASS PATTERNS
• BASED ON ESTIMATED POSTERIOR PROBABILITIES
• Latent classes
• 1 1240.78344 0.16662
• 2 969.53997 0.13019
• 3 4761.71765 0.63941
• 4 474.95894 0.06378
• CLASSIFICATION OF INDIVIDUALS BASED ON MOST
  LIKELY LATENT CLASS MEMBERSHIP
• Latent classes
• 1 1218 0.16356
• 2 650 0.08728
• 3 5075 0.68148

12
Entropy

• CLASSIFICATION QUALITY
• Entropy 0.732
• Average Latent Class Probabilities for Most
  Likely Latent Class Membership (Row) by Latent
  Class (Column)
• 1 2 3 4
• 1 0.814 0.031 0.122 0.033
• 2 0.048 0.850 0.042 0.060
• 3 0.029 0.067 0.904 0.000
• 4 0.145 0.074 0.000 0.781

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Entropy

• CLASSIFICATION QUALITY
• Entropy 0.732
• Average Latent Class Probabilities for Most
  Likely Latent Class Membership (Row) by Latent
  Class (Column)
• 1 2 3 4
• 1 0.814 0.031 0.122 0.033
• 2 0.048 0.850 0.042 0.060
• 3 0.029 0.067 0.904 0.000
• 4 0.145 0.074 0.000 0.781

Not a weighted average!!
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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
• -------------------------------------------------
  --------------------------

15
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
• -------------------------------------------------
  --------------------------

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
• -------------------------------------------------
  --------------------------

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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
• -------------------------------------------------
  -------------------------

18
4-class model trajectories
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Multinomial model

• Multinomial logistic regression
  Number of obs 6331
• 
  LR chi2(3) 22.31
• 
  Prob gt chi2 0.0001
• Log likelihood -6450.991
  Pseudo R2 0.0017
• --------------------------------------------------
  ------------------------------
• class RRR Std. Err. z
  Pgtz 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
• --------------------------------------------------
  ------------------------------
• (classNon Bed-share is the base outcome)

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Latent Class Growth Analysis
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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

24
LCGA in Mplus

• Shorthand
• i s q y1_at_0 y2_at_1 y3_at_2 y4_at_3 y5_at_4
• Longhand
• i by y1_at_0 y2_at_0 y3_at_0 y4_at_0 y5_at_0
• s by y1_at_0 y2_at_1 y3_at_2 y4_at_3 y5_at_4
• q by y1_at_0 y2_at_2 y3_at_4 y4_at_9 y5_at_16
• y1-y5_at_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)

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Choosing the growth parameters

• With LLCA there are no choices to be made
  regarding how to describe/parameterize the
  trajectories they dont 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.

26
Choosing the factor loadings

• We have five repeated measures
• 1, 6, 18, 30 and 42 months
• Options
• i s q bedt1_at_1 bedt2_at_6 bedt3_at_18 bedt4_at_30
  bedt5_at_42
• i s q bedt1_at_0 bedt2_at_5 bedt3_at_17 bedt4_at_29
  bedt5_at_41
• i s q bedt1_at_0.083 bedt2_at_0.5 bedt3_at_1.5
  bedt4_at_2.5 bedt5_at_3.5

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Effect of different choices (4 class)

• i s q beds_ka_at_1 beds_kb_at_6 beds_kd_at_18 beds_kf_at_30
  beds_kj_at_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

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Effect of different choices (4 class)

• i s q beds_ka_at_0.083 beds_kb_at_0.5 beds_kd_at_1.5
  beds_kf_at_2.5 beds_kj_at_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

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• 4-class MODEL RESULTS
• 
  Two-Tailed
• Estimate S.E.
  Est./S.E. P-Value
• Latent Class 1
• I
• BEDS_t1 1.000 0.000
  999.000 999.000
• BEDS_t2 1.000 0.000
  999.000 999.000
• BEDS_t3 1.000 0.000
  999.000 999.000
• BEDS_t4 1.000 0.000
  999.000 999.000
• BEDS_t5 1.000 0.000
  999.000 999.000
• S
• BEDS_t1 0.083 0.000
  999.000 999.000
• BEDS_t2 0.500 0.000
  999.000 999.000
• BEDS_t3 1.500 0.000
  999.000 999.000
• BEDS_t4 2.500 0.000
  999.000 999.000

All fixed (not estimated)
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• 4-class MODEL RESULTS
• 
  Two-Tailed
• Estimate S.E.
  Est./S.E. P-Value
• Latent Class 1
• Means
• I 2.001 0.144
  13.876 0.000
• S 1.452 0.146
  9.975 0.000
• Q -0.311 0.037
  -8.319 0.000
• Thresholds
• BEDS_t11 2.662 0.086
  31.010 0.000
• BEDS_t21 2.662 0.086
  31.010 0.000
• BEDS_t31 2.662 0.086
  31.010 0.000
• BEDS_t41 2.662 0.086
  31.010 0.000

Estimated different across classes
Estimated equal across classes
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4-class LCGA model
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4-class LCGA model
These are all quadratics!
33
Comparison with LLCA result
LCGA LLCA
Entropy 0.805 aBIC 30241.3
Entropy 0.732 aBIC 30260.3
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Comparison with LLCA result
LCGA LLCA
Entropy 0.805 aBIC 30241.3
Entropy 0.732 aBIC 30260.3
Curves may look similar(ish), but check class
distribution and pattern assignment
35
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

36
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

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Output tech1

• PARAMETER SPECIFICATION FOR LATENT CLASS
  INDICATOR GROWTH MODEL PART
• ALPHA(F) FOR LATENT CLASS 1
• I S Q
• ________ ________
  ________
• 1 2 3 4
• ALPHA(F) FOR LATENT CLASS 2
• I S Q
• ________ ________
  ________
• 1 5 6 7
• ALPHA(F) FOR LATENT CLASS 3
• I S Q

38
Constrain a q to be zero

• OVERALL
• i s q beds_ka_at_0.083 beds_kb_at_0.5
• beds_kd_at_1.5 beds_kf_at_2.5 beds_kj_at_3.5
• c1
• q_at_0
• Then re-run the model doesnt always work!!!

39
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