use "simulated_multilevel_data.dta", clear2 Two Level Cross Sectional; And Three Level Longitudinal Models
2.1 Cross Sectional Model
2.1.1 Get Data
2.1.2 The Equation
\[\text{outcome}_{ij} = \beta_0 + \beta_1 \text{parental warmth} + \beta_2 \text{physical punishment} + \beta_3 \text{time} + \]
\[\beta_4 \text{identity}_2 + \beta_5 \text{intervention} + \beta_6 HDI +\]
\[u_{0j} + u_{1j} \times \text{parental warmth} + e_{ij} \]
2.1.3 Descriptive Statistics
summarize // descriptive statistics Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
country | 3,000 15.5 8.656884 1 30
HDI | 3,000 64.76667 17.24562 33 87
family | 3,000 50.5 28.87088 1 100
id | 0
identity | 3,000 .4976667 .5000779 0 1
-------------+---------------------------------------------------------
intervention | 3,000 .4843333 .4998378 0 1
physical_p~t | 3,000 2.478667 1.360942 0 5
warmth | 3,000 3.521667 1.888399 0 7
outcome | 3,000 52.43327 6.530996 29.60798 74.835532.1.4 Spaghetti Plot
spagplot outcome warmth, id(country) scheme(stcolor)
graph export spagplot1.png, width(1000) replace
2.1.5 Unconditional Model
2.1.5.1 Model
mixed outcome || country: // unconditional modelPerforming EM optimization ...
Performing gradient-based optimization:
Iteration 0: Log likelihood = -9802.8371
Iteration 1: Log likelihood = -9802.8371
Computing standard errors ...
Mixed-effects ML regression Number of obs = 3,000
Group variable: country Number of groups = 30
Obs per group:
min = 100
avg = 100.0
max = 100
Wald chi2(0) = .
Log likelihood = -9802.8371 Prob > chi2 = .
------------------------------------------------------------------------------
outcome | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_cons | 52.43327 .3451217 151.93 0.000 51.75685 53.1097
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
country: Identity |
var(_cons) | 3.178658 .9226737 1.799552 5.614658
-----------------------------+------------------------------------------------
var(Residual) | 39.46106 1.024013 37.50421 41.52
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 166.31 Prob >= chibar2 = 0.00002.1.5.2 ICC
estat iccIntraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
country | .0745469 .0201254 .0434963 .1248696
------------------------------------------------------------------------------2.1.6 Conditional Model
mixed outcome warmth physical_punishment identity i.intervention HDI || country: warmth // multilevel model
est store crosssectional // store estimatesPerforming EM optimization ...
Performing gradient-based optimization:
Iteration 0: Log likelihood = -9626.6279
Iteration 1: Log likelihood = -9626.607
Iteration 2: Log likelihood = -9626.607
Computing standard errors ...
Mixed-effects ML regression Number of obs = 3,000
Group variable: country Number of groups = 30
Obs per group:
min = 100
avg = 100.0
max = 100
Wald chi2(5) = 334.14
Log likelihood = -9626.607 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------
outcome | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------------+----------------------------------------------------------------
warmth | .8345368 .0637213 13.10 0.000 .7096453 .9594282
physical_punishment | -.9916657 .0797906 -12.43 0.000 -1.148052 -.8352791
identity | -.3004767 .2170295 -1.38 0.166 -.7258466 .1248933
1.intervention | .6396427 .2174519 2.94 0.003 .2134448 1.065841
HDI | -.003228 .0199257 -0.16 0.871 -.0422817 .0358256
_cons | 51.99991 1.371257 37.92 0.000 49.3123 54.68753
-------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
country: Independent |
var(warmth) | .0227504 .0257784 .0024689 .2096436
var(_cons) | 2.963975 .9737647 1.556777 5.643163
-----------------------------+------------------------------------------------
var(Residual) | 34.97499 .9097109 33.23668 36.80422
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 205.74 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.2.2 Longitudinal Model
2.2.1 Get Data
use "simulated_multilevel_longitudinal_data.dta", clear2.2.2 The Equation
\[\text{outcome}_{ij} = \beta_0 + \beta_1 \text{parental warmth} + \beta_2 \text{physical punishment} + \beta_3 \text{time} + \]
\[\beta_4 \text{identity}_2 + \beta_5 \text{intervention} + \beta_5 HDI +\]
\[u_{0j} + u_{1j} \times \text{parental warmth} + \]
\[v_{0i} + v_{1i} \times t + e_{ij} \]
2.2.3 Descriptive Statistics
summarize // descriptive statistics Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
country | 9,000 15.5 8.655922 1 30
HDI | 9,000 64.76667 17.2437 33 87
family | 9,000 50.5 28.86767 1 100
id | 0
identity | 9,000 .4976667 .5000223 0 1
-------------+---------------------------------------------------------
intervention | 9,000 .4843333 .4997823 0 1
t | 9,000 2 .8165419 1 3
physical_p~t | 9,000 2.485333 1.373639 0 5
warmth | 9,000 3.514222 1.8839 0 7
outcome | 9,000 53.37768 6.572285 29.60798 79.021992.2.4 Alternate Plot
encode id, generate(idNUMERIC) // numeric version of id
* spagplot outcome t if idNUMERIC <= 10, id(idNUMERIC) scheme(stcolor)
twoway (lfit outcome t) (scatter outcome t) if idNUMERIC <= 10, by(idNUMERIC) scheme(stcolor)
graph export spagplot2.png, width(1000) replace
2.2.5 Unconditional Model
2.2.5.1 Model
mixed outcome || country: || id: // unconditional model2.2.5.2 ICC
estat iccIntraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
country | .0748336 .0190847 .0450028 .1219141
id|country | .3462837 .0171461 .3134867 .3806097
------------------------------------------------------------------------------2.2.6 Conditional Model
mixed outcome t warmth physical_punishment i.identity i.intervention HDI || country: warmth || id: t // multilevel model
est store longitudinal // store estimatesPerforming EM optimization ...
Performing gradient-based optimization:
Iteration 0: Log likelihood = -28523.49
Iteration 1: Log likelihood = -28499.987
Iteration 2: Log likelihood = -28499.739
Iteration 3: Log likelihood = -28499.604
Iteration 4: Log likelihood = -28499.603
Computing standard errors ...
Mixed-effects ML regression Number of obs = 9,000
Grouping information
-------------------------------------------------------------
| No. of Observations per group
Group variable | groups Minimum Average Maximum
----------------+--------------------------------------------
country | 30 300 300.0 300
id | 3,000 3 3.0 3
-------------------------------------------------------------
Wald chi2(6) = 1096.15
Log likelihood = -28499.603 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------
outcome | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------------+----------------------------------------------------------------
t | .943864 .0658716 14.33 0.000 .814758 1.07297
warmth | .9134959 .0423732 21.56 0.000 .830446 .9965459
physical_punishment | -1.007897 .0497622 -20.25 0.000 -1.105429 -.9103647
1.identity | -.1276926 .1515835 -0.84 0.400 -.4247908 .1694057
1.intervention | .8589966 .1519095 5.65 0.000 .5612596 1.156734
HDI | -.0005657 .0196437 -0.03 0.977 -.0390666 .0379352
_cons | 50.46724 1.338318 37.71 0.000 47.84418 53.09029
-------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
country: Independent |
var(warmth) | .0107586 .0127845 .0010478 .1104703
var(_cons) | 3.167085 .9146761 1.798154 5.578181
-----------------------------+------------------------------------------------
id: Independent |
var(t) | 3.58e-09 7.06e-07 3.5e-177 3.7e+159
var(_cons) | 8.387275 .4724188 7.510631 9.366242
-----------------------------+------------------------------------------------
var(Residual) | 26.02733 .4753701 25.11211 26.97592
------------------------------------------------------------------------------
LR test vs. linear model: chi2(4) = 1247.03 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.2.3 Nice Table of Results
etable, estimates(crosssectional longitudinal) ///
showstars showstarsnote /// show stars and note
column(estimate) // column is modelname crosssectional longitudinal
----------------------------------------------------------------
parental warmth in past week 0.835 ** 0.913 **
(0.064) (0.042)
physical punishment in past week -0.992 ** -1.008 **
(0.080) (0.050)
hypothetical identity group variable -0.300
(0.217)
recieved intervention
1 0.640 ** 0.859 **
(0.217) (0.152)
Human Development Index -0.003 -0.001
(0.020) (0.020)
time 0.944 **
(0.066)
hypothetical identity group variable
1 -0.128
(0.152)
Intercept 52.000 ** 50.467 **
(1.371) (1.338)
var(warmth) 0.023 0.011
(0.026) (0.013)
var(_cons) 2.964 3.167
(0.974) (0.915)
var(e) 34.975 26.027
(0.910) (0.475)
var(_cons) 8.387
(0.472)
var(t) 0.000
(0.000)
Number of observations 3000 9000
----------------------------------------------------------------
** p<.01, * p<.05