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, | 3,780 | | Hi | 2, | 2,551 | | Total | 5, | 6,331 | | Pearson chi2(1) = Pr = 0.000

C/S association – t2 S-class | Not bed-sh Bed-sh | Total Lo | 3, | 3,780 | | Hi | 2, | 2,551 | | Total | 5, | 6,331 | | Pearson chi2(1) = Pr = 0.310

C/S association – t3 S-class | Not bed-sh Bed-sh | Total Lo | 3, | 3,780 | | Hi | 2, | 2,551 | | Total | 5,238 1,093 | 6,331 | | Pearson chi2(1) = Pr = 0.000

C/S association – t4 S-class | Not bed-sh Bed-sh | Total Lo | 2, | 3,780 | | Hi | 2, | 2,551 | | Total | 4,968 1,363 | 6,331 | | Pearson chi2(1) = Pr = 0.000

C/S association – t5 S-class | Not bed-sh Bed-sh | Total Lo | 2, | 3,780 | | Hi | 2, | 2,551 | | Total | 5,008 1,323 | 6,331 | | Pearson chi2(1) = Pr = 0.001

Model fit stats 1 class2 class3 class4 class5 class Estimated params H0 Likelihood aBIC Entropy Tech BLRT statistic BLRT p-value -< 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 CLASSIFICATION OF INDIVIDUALS BASED ON MOST LIKELY LATENT CLASS MEMBERSHIP Latent classes

Entropy CLASSIFICATION QUALITY Entropy Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column)

Entropy CLASSIFICATION QUALITY Entropy Average Latent Class Probabilities for Most Likely Latent Class Membership (Row) by Latent Class (Column) 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 | | | | | | | | | | | | |

Class 2 (13.0%) | bed_t1 bed_t2 bed_t3 bed_t4 bed_t5 p_c1 p_c2 p_c3 p_c4 num | | | | | | | | | | | | | | | | | | | | |

Class 3 (63.9%) | bed_t1 bed_t2 bed_t3 bed_t4 bed_t5 p_c1 p_c2 p_c3 p_c4 num | | | | | | | | | | | | | | | | | | |

Class 4 (6.4%) | bed_t1 bed_t2 bed_t3 bed_t4 bed_t5 p_c1 p_c2 p_c3 p_c4 num | | | | | | | | | | | | | | | | | | | | | | |

4-class model ‘trajectories’

Multinomial model Multinomial logistic regression Number of obs = 6331 LR chi2(3) = Prob > chi2 = Log likelihood = Pseudo R2 = class | RRR Std. Err. z P>|z| [95% Conf. Interval] Always Bed-sh | Hi Soc Class | Early Bed-sh | Hi Soc Class | Late Bed-sh | Hi Soc Class | (class==Non Bed-share is the base outcome)

Latent Class Growth Analysis

T1T2T3T4T5 C Outcome Risk factors

T1T2T3T4T5 isq 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 | Longhand i by s by q by 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 | i s q | i s q |

Effect of different choices (4 class) i s q | perturbed starting value run(s) did not converge. Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: 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 | 21 perturbed starting value run(s) did not converge. Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: THE MODEL ESTIMATION TERMINATED NORMALLY

4-class MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Latent Class 1 I | BEDS_t BEDS_t BEDS_t BEDS_t BEDS_t S | BEDS_t BEDS_t BEDS_t BEDS_t BEDS_t Q | BEDS_t BEDS_t BEDS_t BEDS_t BEDS_t All fixed (not estimated)

4-class MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value Latent Class 1 Means I S Q Thresholds BEDS_t1$ BEDS_t2$ BEDS_t3$ BEDS_t4$ BEDS_t5$ Estimated + different across classes Estimated + equal across classes

4-class LCGA model

These are all quadratics!

Comparison with LLCA result LCGALLCA Entropy = aBIC = Entropy = aBIC =

Comparison with LLCA result LCGALLCA Entropy = aBIC = Entropy = aBIC = 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 ________ ________ ________ ALPHA(F) FOR LATENT CLASS 2 I S Q ________ ________ ________ ALPHA(F) FOR LATENT CLASS 3 I S Q ________ ________ ________

Constrain a ‘q’ to be zero %OVERALL% i s q | %c#1% 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