Dear all,

Would you help me to interpret the following models?

This is 5 waves data with time-varying treatment (0 to 2 scale) and two covariates.

In M1, I run two-way fixed effect model. But I could not find any significant treatment effect (-.002). As an alternative specification, I run the following model - I created the interaction term between treatment and time. In M2, a one unit increase in treatment variable "on average" is associated with .28*** increase in math achievement. Yet, the interaction term in M2 shows that every year treatment effect decreases by .09.

Here is my questions:

1) In M2, it seems that the main treatment effect (.28) corresponds to "year 1 effect". So after 4 years, the treatment effect turns to be negative (-.36+.28=-.08). Am I right?

2) In M1, treatment effect is found to be -.002. It is usually interpreted as "on overage" one unit increase in X is associated with Y. What does "on average" exactly stand for? In every year, treatment variable has -.002 effect? Thus, over 4 years, it has -.002*4 total effects?

3) If I rely on M3, it seems clear that treatment effect become more detrimental over years. If I want to manually calculate the treatment effect over 4 years, should I only employ significant coefficients associated with treatment variable? e.g., .19+(-.18-.30-.33) ?


Your reply will be greatly appreciated. Thank you!


Sean




M1

Math Coef. Std. Err. t P>t [95% Conf. Interval]

Treatment -.0018498 .0220533 -0.08 0.933 -.045076 .0413765
IRT_R .0006786 .0013973 0.49 0.627 .0020602 .0034174
IRT_M -.0060498 .0015313 -3.95 0.000 .0090514 -.0030483

year
_W4 .5765732 .0505503 11.41 0.000 .4774903 .6756561
_W6 1.355762 .0760639 17.82 0.000 1.20667 1.504853
_W7 2.224214 .094319 23.58 0.000 2.039341 2.409087
_W8 3.107438 .1060079 29.31 0.000 2.899653 3.315222

_cons 16.75458 .1074408 155.94 0.000 16.54399 16.96517



M2

Math Coef. Std. Err. t P>t [95% Conf. Interval]

cov1 .0002283 .0013969 0.16 0.870 -.0025098 .0029664
cov2 -.0057629 .0015299 -3.77 0.000 -.0087616 -.0027641

year
_W4 .5955138 .0505553 11.78 0.000 .4964211 .6946065
_W6 1.400425 .0762236 18.37 0.000 1.25102 1.549829
_W7 2.303995 .0948584 24.29 0.000 2.118064 2.489925
_W8 3.233523 .1073338 30.13 0.000 3.023139 3.443906

Treatment .2819542 .0454272 6.21 0.000 .1929129 .3709955

c.year#c.Treatment -.0880109 .012321 -7.14 0.000 -.112161 -.0638608

_cons 16.72663 .107375 155.78 0.000 16.51616 16.93709




M3

Math Coef. Std. Err. t P>t [95% Conf. Interval]

cov1 .0002339 .0013978 0.17 0.867 -.0025059 .0029736
cov2 -.0057813 .0015312 -3.78 0.000 -.0087826 -.0027799

year
_W4 .5898591 .051925 11.36 0.000 .4880817 .6916365
_W6 1.401499 .077243 18.14 0.000 1.250096 1.552902
_W7 2.317785 .0956012 24.24 0.000 2.130399 2.505172
_W8 3.22343 .1076846 29.93 0.000 3.012359 3.434501

year#c.Treatment
_W4 -.0665615 .0551084 -1.21 0.227 -.1745786 .0414557
_W6 -.1763148 .0546061 -3.23 0.001 -.2833474 -.0692823
_W7 -.2952571 .0555001 -5.32 0.000 -.4040421 -.1864721
_W8 -.3270771 .0556028 -5.88 0.000 -.4360634 -.2180909

Treatment .1907644 .045256 4.22 0.000 .1020589 .27947

_cons 16.72785 .1080214 154.86 0.000 16.51612 16.93958