Method Introduction

HTKS, Mr.Ant, DCCS

Some outcomes are categorical and contain many zeros (e.g. HTKS contains 102/218 zeros), thus we use zero-inflated model to fit them: Firstly, we use a binary model to fit “zero or not”, secondly we use poisson / quasi poisson model to fit the distribution.

And the interpretation of model can be: In the first step, binary model can represent “whether the children understand the game”, if he/she understood, then score is likely to be non-zero, otherwise zero; then in the second step, the poisson model can estimate the ability of children in this area / outcome.

Negativity and Lability, Emotional Regulation, CBC_AVG

Linear mixed longitudinal model is used.

HTKS

Zero-inflation Model

Treatment is significantly positive (Estimate = 0.941, p value = 0.038), i.e. receiving treatment will increase the probability of achieving non-zero score or “understanding the HTKS game”.

Other covariates are not significant.

Conditional Model (Given non-zero “ability”)

Baseline age (the age when children join the experiment) is significantly positive (Estimate = 0.102, p value = 0.004): older children are more likely to behave better. We are using linear term because no significant non-linear trend is discovered yet.

Sex & Time interaction is significantly positive (Estimate = 0.625, p value = 0.008): girls’ time effect is stronger than boys’. Here the time effect means their changed ability from time point 1 to time point 2, due to children are getting older.

Baseline age & Treatment interaction is significantly negative (Estimate = -0.122, p value = 0) : the baseline age will influence the effect of treatment. In the sense of average, children with baseline age smaller than 55 months have positive treatment effect, while those with baseline age bigger than 55 months have negative treatment effects.

Mr. Ant Acc

Zero-inflation Model

Time effect is significantly positive (Estimate = 1.246, p value = 0.031), i.e. Compared with period 1, the period 2’s children have greater probability of achieving non-zero score or “understanding the HTKS game”.

Other covariates are not significant.

Conditional Model (Given non-zero “ability”)

Covariates are not significant.

Mr. Ant Pt

Zero-inflation Model

Time effect is significantly positive (Estimate = 1.266, p value = 0.028), i.e. Compared with period 1, the period 2’s children have greater probability of achieving non-zero score or “understanding the HTKS game”.

Other covariates are not significant.

Conditional Model (Given non-zero “ability”)

Covariates are not significant.

DCCS

Zero-inflation Model

Time effect is significantly positive (Estimate = 1.629, p value = 0.001), i.e. Compared with period 1, the period 2’s children have greater probability of achieving non-zero score or “understanding the HTKS game”.

Other covariates are not significant.

Conditional Model (Given non-zero “ability”)

Sex effect is significantly positive (Estimate = 0.366, p value = 0.002): Girls are more likely to behave better.

CBC_AVG (Total average child behavior checklist)

No significant result.

Emoreg (Emotional Regulation)

There is significant difference between grils and boys about the time effecet (Estimate = 0.437, p value = 0) and treatment effect (Estimate = -0.374, p value = 0.011).

Girls

Time effect is significant (Estimate = 0.22, p value = 0.023).

Treatment effect is not significant (Estimate = -0.1, p value = 0.399).

Boys

Time effect is significant (Estimate = -0.217, p value = 0.003).

Treatment effect is significant (Estimate = 0.275, p value = 0.002).

NegLibiliy (Negativity and Lability)

There is significant difference between grils and boys about the time effecet (Estimate = -0.397, p value = 0) and treatment effect (Estimate = 0.342, p value = 0.012).

Girls

Time effect is significant (Estimate = -0.283, p value = 0.001).

Treatment effect is significant (Estimate = 0.221, p value = 0.043).

Boys

Time effect is not significant (Estimate = 0.114, p value = 0.082).

Treatment effect is not significant (Estimate = -0.121, p value = 0.132).

Supplement

HTKS

## table of HTKS (using paired data only, removing missing data):
## 
##  0  1  2  3  4  5  6  7  8 10 11 12 13 14 16 17 18 19 20 21 22 23 26 27 29 30 
## 95  6 20  5  6  1  3  1  8  4  1  4  2  7  4  2  2  2  3  2  4  1  1  1  2  2 
## 31 32 34 37 38 40 43 46 47 48 52 
##  1  1  2  3  1  2  2  1  2  1  1

X Estimate Std..Error z.value Pr…z..
(Intercept) 1.8513063 0.1799857 10.2858543 0.0000000
age 0.1020116 0.0350805 2.9079258 0.0036383
Receive_Treatment1 0.0540590 0.1813452 0.2980998 0.7656270
as.factor(Sex)2 0.5022247 0.2750358 1.8260340 0.0678451
as.factor(Time)2 0.1391914 0.1557823 0.8934995 0.3715897
age:Receive_Treatment1 -0.1219787 0.0204133 -5.9754474 0.0000000
Receive_Treatment1:as.factor(Sex)2 -0.3853183 0.2666780 -1.4448823 0.1484910
as.factor(Sex)2:as.factor(Time)2 0.6248874 0.2372206 2.6342035 0.0084335
X Estimate Std..Error z.value Pr…z..
(Intercept) -0.0281903 0.2551570 -0.1104822 0.9120269
age 0.0246011 0.0465180 0.5288501 0.5969094
as.factor(Sex)2 0.4917799 0.3313476 1.4841813 0.1377608
Receive_Treatment1 -0.9408508 0.4546022 -2.0696134 0.0384886
as.factor(Time)2 -0.1326474 0.3983418 -0.3329989 0.7391351

Mr. Ant Acc

X Estimate Std..Error z.value Pr…z..
(Intercept) 1.2489534 0.0944058 13.2296257 0.0000000
age -0.0093135 0.0139759 -0.6663966 0.5051577
Receive_Treatment1 0.0451497 0.1240892 0.3638489 0.7159709
as.factor(Sex)2 -0.0588649 0.1021747 -0.5761200 0.5645341
as.factor(Time)2 0.2198879 0.1232909 1.7834885 0.0745068
X Estimate Std..Error z.value Pr…z..
(Intercept) 0.2637709 0.3999526 0.6595053 0.5095713
age 0.0434761 0.0807657 0.5382988 0.5903708
Receive_Treatment1 0.5494247 0.6401436 0.8582836 0.3907359
as.factor(Sex)2 -0.0330561 0.5591436 -0.0591191 0.9528572
as.factor(Time)2 -1.2455259 0.5764964 -2.1605092 0.0307333

Mr. Ant Pt

X Estimate Std..Error z.value Pr…z..
(Intercept) 1.3843870 0.0943798 14.6682542 0.0000000
age -0.0096918 0.0146161 -0.6630945 0.5072701
Receive_Treatment1 0.0642115 0.1239128 0.5181992 0.6043193
as.factor(Sex)2 -0.0690907 0.1068597 -0.6465549 0.5179201
as.factor(Time)2 0.1983791 0.1193676 1.6619173 0.0965293
X Estimate Std..Error z.value Pr…z..
(Intercept) 0.2814417 0.4006534 0.7024568 0.4823943
age 0.0435913 0.0811134 0.5374113 0.5909835
Receive_Treatment1 0.5556033 0.6403152 0.8677029 0.3855570
as.factor(Sex)2 -0.0282149 0.5610975 -0.0502853 0.9598951
as.factor(Time)2 -1.2656109 0.5760034 -2.1972281 0.0280042

DCCS

X Estimate Std..Error z.value Pr…z..
(Intercept) 1.5031960 0.1031532 14.5724597 0.0000000
age 0.0311040 0.0237259 1.3109743 0.1898665
I(age^2) 0.0007670 0.0043826 0.1750061 0.8610748
Receive_Treatment1 0.0249326 0.1202171 0.2073966 0.8357001
as.factor(Sex)2 0.3663824 0.1165387 3.1438680 0.0016673
as.factor(Time)2 0.1580867 0.1161112 1.3615119 0.1733520
X Estimate Std..Error z.value Pr…z..
(Intercept) 0.3909464 0.2748835 1.4222254 0.1549608
age -0.0320729 0.0736718 -0.4353478 0.6633100
I(age^2) -0.0200076 0.0147120 -1.3599486 0.1738462
Receive_Treatment1 0.2354658 0.4889672 0.4815575 0.6301204
as.factor(Sex)2 0.6054718 0.3384683 1.7888581 0.0736377
as.factor(Time)2 -1.6292918 0.4684072 -3.4783664 0.0005045

CBC_AVG

X Estimate Std..Error t.value
(Intercept) 2.1165913 0.5200362 4.0700847
age 0.0066965 0.0096694 0.6925412
as.factor(Sex)2 0.1339700 0.0680292 1.9693003
as.factor(Time)2 -0.1057525 0.0865136 -1.2223805
Receive_Treatment 0.0965722 0.0943254 1.0238198

Emoreg

X Estimate Std..Error t.value p.value
(Intercept) 3.5364024 0.0691638 51.1307942 0.000
as.factor(Sex)1 -0.0712329 0.0855110 -0.8330265 0.405
as.factor(Time)2 0.2199753 0.0965549 2.2782401 0.023
Receive_Treatment1 -0.0997384 0.1183119 -0.8430120 0.399
as.factor(Sex)1:as.factor(Time)2 -0.4367405 0.1210499 -3.6079385 0.000
as.factor(Sex)1:Receive_Treatment1 0.3744700 0.1470945 2.5457781 0.011
X Estimate Std..Error t.value p.value
(Intercept) 3.4651695 0.0502841 68.9117849 0.000
Sex2 0.0712329 0.0855110 0.8330265 0.405
as.factor(Time)2 -0.2167652 0.0730084 -2.9690465 0.003
Receive_Treatment1 0.2747316 0.0874018 3.1433156 0.002
Sex2:as.factor(Time)2 0.4367405 0.1210499 3.6079385 0.000
Sex2:Receive_Treatment1 -0.3744700 0.1470945 -2.5457781 0.011

NegLibiliy

X Estimate Std..Error t.value p.value
(Intercept) 1.5298212 0.0589436 25.953991 0.000
as.factor(Sex)2 -0.1159690 0.1002369 -1.156950 0.247
as.factor(Time)2 0.1138711 0.0654308 1.740330 0.082
Receive_Treatment1 -0.1211462 0.0804392 -1.506059 0.132
as.factor(Sex)2:as.factor(Time)2 -0.3972181 0.1083321 -3.666670 0.000
as.factor(Sex)2:Receive_Treatment1 0.3418826 0.1353766 2.525419 0.012
X Estimate Std..Error t.value p.value
(Intercept) 1.4138522 0.0810746 17.438909 0.000
Sex1 0.1159690 0.1002369 1.156950 0.247
as.factor(Time)2 -0.2833469 0.0863404 -3.281743 0.001
Receive_Treatment1 0.2207364 0.1088869 2.027208 0.043
Sex1:as.factor(Time)2 0.3972181 0.1083321 3.666670 0.000
Sex1:Receive_Treatment1 -0.3418826 0.1353766 -2.525419 0.012