Social patterning in bed-sharing behaviour

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)

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

Model fit stats 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 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 4 504 0.06768

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

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!!

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’

Multinomial model Multinomial logistic regression Number of obs = 6331 LR chi2(3) = 22.31 Prob > chi2 = 0.0001 Log likelihood = -6450.991 Pseudo R2 = 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 T2 T3 T4 T5 C Outcome Risk factors

T1 T2 T3 T4 T5 i s q C Outcome Risk factors

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 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 BEDS_t5 3.500 0.000 999.000 999.000 Q | BEDS_t1 0.007 0.000 999.000 999.000 BEDS_t2 0.250 0.000 999.000 999.000 BEDS_t3 2.250 0.000 999.000 999.000 BEDS_t4 6.250 0.000 999.000 999.000 BEDS_t5 12.250 0.000 999.000 999.000 All fixed (not estimated)

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_t1$1 2.662 0.086 31.010 0.000 BEDS_t2$1 2.662 0.086 31.010 0.000 BEDS_t3$1 2.662 0.086 31.010 0.000 BEDS_t4$1 2.662 0.086 31.010 0.000 BEDS_t5$1 2.662 0.086 31.010 0.000 Estimated + different across classes Estimated + equal across classes

4-class LCGA model

4-class LCGA model These are all quadratics!

Comparison with LLCA result LCGA LLCA Entropy = 0.805 aBIC = 30241.3 Entropy = 0.732 aBIC = 30260.3

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

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 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 ________ ________ ________ 1 8 9 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

Social patterning in bed-sharing behaviour