Dear all,
I want to investigate which child in a sibling group takes over the care of a parent. The focus is on gender (of both the caregiving child and the siblings), but other characteristics of the children and siblings (e.g., education, employment status, own children, spatial proximity to the parent) will also be examined as influencing factors. To do so, I use a multilevel design that first includes characteristics of the child (individual level), then characteristics of sliblings and the parent (contextual level), and finally cross-level interactions between child gender and sibling characteristics.
So far I have computed a null model (with the dependent variable only) and a random intercept model with additional independent individual-level variables. The next step is to test random slopes, assuming that some effects of the individual-level variables vary across families. I chose child gender as one of these variables, resulting in the following command:
However, I just don't know which covariance structure is the right one. The literature tells me that I should use covariance(unstructured) if I assume that the slope in a family is related to the family-specific intercept (i.e., it is plausible that, for example, the effect of a variable is particularly high (or low) in those families that have a high overall level of the dependent variable (intercept)). I am not sure of this assumption, and comparing the covariance(unstructured) and covariance(independent) options I get the following results (the first model is the random intercept model, second and third are the random slopes models):
Does anyone have any advice or idea which covariance structure to choose? LR tests (comparison with random intercept model) show the following (which I'm also not quite sure how to interpret):
I would appreciate any advice, hint or literature! Thank you!
I want to investigate which child in a sibling group takes over the care of a parent. The focus is on gender (of both the caregiving child and the siblings), but other characteristics of the children and siblings (e.g., education, employment status, own children, spatial proximity to the parent) will also be examined as influencing factors. To do so, I use a multilevel design that first includes characteristics of the child (individual level), then characteristics of sliblings and the parent (contextual level), and finally cross-level interactions between child gender and sibling characteristics.
So far I have computed a null model (with the dependent variable only) and a random intercept model with additional independent individual-level variables. The next step is to test random slopes, assuming that some effects of the individual-level variables vary across families. I chose child gender as one of these variables, resulting in the following command:
Code:
mixed ch_helpfreq_abs i.ch_female i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn || mergeid: ch_female if sample_mixedsibship==1
Code:
* Random Intercept Model
. mixed ch_helpfreq_abs i.ch_female i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn || mergeid: if sample_mixedsibship==1
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -7389.1406
Iteration 1: log likelihood = -7387.197
Iteration 2: log likelihood = -7387.183
Iteration 3: log likelihood = -7387.1829
Computing standard errors:
Mixed-effects ML regression Number of obs = 1,594
Group variable: mergeid Number of groups = 610
Obs per group:
min = 2
avg = 2.6
max = 7
Wald chi2(12) = 42.99
Log likelihood = -7387.1829 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
ch_helpfreq~s | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ch_female |
1. Yes | .0599162 1.368017 0.04 0.965 -2.621349 2.741181
|
ch_employment |
Employed p.. | -1.086707 2.433934 -0.45 0.655 -5.857131 3.683717
Employed f.. | -.3078154 1.989507 -0.15 0.877 -4.207177 3.591546
|
ch_partner |
1. Yes | -1.500792 1.598286 -0.94 0.348 -4.633374 1.631791
ch_nrkids_z | -.1023356 .6575589 -0.16 0.876 -1.391127 1.186456
|
ch_proximity |
Lives up t.. | -6.213011 1.861449 -3.34 0.001 -9.861383 -2.564639
Lives more.. | -9.550823 1.933551 -4.94 0.000 -13.34051 -5.761132
|
ch_educhigh |
1. Yes | 2.241788 1.390524 1.61 0.107 -.4835893 4.967164
|
transfer_ch~r |
1. Yes | 7.237481 4.610893 1.57 0.116 -1.799704 16.27467
|
transfer_pa~d |
1. Yes | 2.592943 1.704474 1.52 0.128 -.7477638 5.93365
ch_age_z | .2604631 .0763616 3.41 0.001 .1107971 .410129
|
ch_birthord~n |
1. Yes | -2.187632 1.277946 -1.71 0.087 -4.69236 .3170947
_cons | 10.57548 2.571127 4.11 0.000 5.536166 15.6148
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Identity |
var(_cons) | 56.34965 26.61961 22.32457 142.2326
-----------------------------+------------------------------------------------
var(Residual) | 568.7814 30.22118 512.5289 631.208
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 4.37 Prob >= chibar2 = 0.0183
.
Code:
* Random Slopes Model (covariance independent)
. mixed ch_helpfreq_abs i.ch_female i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn || mergeid: ch_female if sample_mixedsibship==1
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -7415.2834
Iteration 1: log likelihood = -7413.7116
Iteration 2: log likelihood = -7387.8262
Iteration 3: log likelihood = -7387.1909
Iteration 4: log likelihood = -7387.183
Iteration 5: log likelihood = -7387.1829
Computing standard errors:
Mixed-effects ML regression Number of obs = 1,594
Group variable: mergeid Number of groups = 610
Obs per group:
min = 2
avg = 2.6
max = 7
Wald chi2(12) = 42.99
Log likelihood = -7387.1829 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
ch_helpfreq~s | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ch_female |
1. Yes | .0599162 1.368018 0.04 0.965 -2.621349 2.741181
|
ch_employment |
Employed p.. | -1.086709 2.433934 -0.45 0.655 -5.857132 3.683715
Employed f.. | -.307816 1.989507 -0.15 0.877 -4.207178 3.591545
|
ch_partner |
1. Yes | -1.500791 1.598286 -0.94 0.348 -4.633374 1.631791
ch_nrkids_z | -.1023359 .6575589 -0.16 0.876 -1.391128 1.186456
|
ch_proximity |
Lives up t.. | -6.213011 1.861449 -3.34 0.001 -9.861383 -2.564639
Lives more.. | -9.550823 1.933551 -4.94 0.000 -13.34051 -5.761132
|
ch_educhigh |
1. Yes | 2.241787 1.390524 1.61 0.107 -.4835896 4.967164
|
transfer_ch~r |
1. Yes | 7.237477 4.610892 1.57 0.116 -1.799706 16.27466
|
transfer_pa~d |
1. Yes | 2.592943 1.704473 1.52 0.128 -.7477631 5.93365
ch_age_z | .2604631 .0763615 3.41 0.001 .1107972 .4101289
|
ch_birthord~n |
1. Yes | -2.187632 1.277946 -1.71 0.087 -4.692359 .3170957
_cons | 10.57548 2.571127 4.11 0.000 5.536165 15.6148
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Independent |
var(ch_fem~e) | 3.86e-12 6.57e-12 1.37e-13 1.09e-10
var(_cons) | 56.3494 26.61937 22.32456 142.2314
-----------------------------+------------------------------------------------
var(Residual) | 568.7816 30.22114 512.5291 631.2081
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 4.37 Prob > chi2 = 0.1123
Note: LR test is conservative and provided only for reference.
.
Code:
* Random Slopes Model (covariance unstructured)
. mixed ch_helpfreq_abs i.ch_female i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn || mergeid: ch_female if sample_mixedsibship==1, covariance(unstructured)
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -7367.5075
Iteration 1: log likelihood = -7367.1975
Iteration 2: log likelihood = -7367.1972
Computing standard errors:
Mixed-effects ML regression Number of obs = 1,594
Group variable: mergeid Number of groups = 610
Obs per group:
min = 2
avg = 2.6
max = 7
Wald chi2(12) = 38.61
Log likelihood = -7367.1972 Prob > chi2 = 0.0001
-------------------------------------------------------------------------------
ch_helpfreq~s | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
ch_female |
1. Yes | .2128865 1.535286 0.14 0.890 -2.796218 3.221991
|
ch_employment |
Employed p.. | -.8553566 2.245717 -0.38 0.703 -5.256881 3.546168
Employed f.. | .0740456 1.862312 0.04 0.968 -3.57602 3.724111
|
ch_partner |
1. Yes | -1.587934 1.48168 -1.07 0.284 -4.491974 1.316106
ch_nrkids_z | -.1332578 .6052143 -0.22 0.826 -1.319456 1.05294
|
ch_proximity |
Lives up t.. | -6.412381 1.75511 -3.65 0.000 -9.852333 -2.972429
Lives more.. | -8.642698 1.832243 -4.72 0.000 -12.23383 -5.051568
|
ch_educhigh |
1. Yes | 2.098393 1.354806 1.55 0.121 -.5569777 4.753763
|
transfer_ch~r |
1. Yes | 7.01759 4.670133 1.50 0.133 -2.135702 16.17088
|
transfer_pa~d |
1. Yes | 1.976084 1.718355 1.15 0.250 -1.39183 5.343998
ch_age_z | .2672349 .0804098 3.32 0.001 .1096345 .4248353
|
ch_birthord~n |
1. Yes | -2.104678 1.177986 -1.79 0.074 -4.413489 .2041318
_cons | 10.37321 2.514511 4.13 0.000 5.444861 15.30156
-------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Unstructured |
var(ch_fem~e) | 776.4265 93.19707 613.66 982.3651
var(_cons) | 462.2535 48.25712 376.72 567.2072
cov(ch_fem~e,_cons) | -426.8151 54.35742 -533.3536 -320.2765
-----------------------------+------------------------------------------------
var(Residual) | 261.2165 24.53399 217.2972 314.0127
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 44.34 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
Code:
*Comparison: Model with covariance(independent)
. lrtest femrand2 ri
Likelihood-ratio test LR chi2(1) = -0.00
(Assumption: ri nested in femrand2) Prob > chi2 = 1.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on
the boundary of the parameter space. If this is not true, then the
reported test is conservative.
Code:
*Comparison: Model with covariance(unstructured)
. lrtest femrand1 ri
Likelihood-ratio test LR chi2(2) = 39.97
(Assumption: ri nested in femrand1) Prob > chi2 = 0.0000
Note: The reported degrees of freedom assumes the null hypothesis is not on
the boundary of the parameter space. If this is not true, then the
reported test is conservative.
