Multiple treatment effects - ITT

[Margarita Espinoza]

Dear All,

I have implemented an RCT with two treatments. However, I am troubled with the analysis part.
Differences in means suggest that I have an positive impacts in my different outcomes. However, I would like to show this by estimating the ITT, in a single OLS regression.
I heard that running one OLS with the two treatments gives unbiased estimates. Moreover, I found that in multiple treatment specifications (Wooldridge, 2007) we could use IV.
Could it be the random assigment an IV?

Another questions is whether the specification of my treatment variables are correct. I am only using the data from the second period (post) and using T1 = 1 if receive treatment 1, then T2 = 1 if receive treatment 2. In the model I am not including the control variable. Is this correct?

the model looks like

Y = T1 + T2 + e

Thank you and looking forward for your advise !
Best

[Roman Mostazir]

Dear All,

Another questions is whether the specification of my treatment variables are correct. I am only using the data from the second period (post) and using T1 = 1 if receive treatment 1, then T2 = 1 if receive treatment 2. In the model I am not including the control variable. Is this correct?

the model looks like

Y = T1 + T2 + e

Thank you and looking forward for your advise !
Best

If you are estimating ITT (Intention to Treat) effect, your model must include randomisation/Treatment arms as the group variable regardless wheter they received the treatment or not. Otherwise, you will have biased estimate. For future, please provide data example of your data using -dataex-. Please see the FAQ section on how to post properly to get a good reply.

[Margarita Espinoza]

Dear Roman,
Thank you for your quick answer.

Here is an example for the ITT of one of my outcomes. I am estimating the probability to use fertilizer by comparing two treatments. One treatment is extension and the other treatment is extension plus fertilizer. Each treatment variable is defined by the randomization assignment, and the outcome is a continuous variable ranging from 1 to 0.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float(exp treatment_1 treatment_2)
  1 1 0
 .6 1 0
.25 1 0
 .5 0 1
 .5 0 1
.95 0 1
 .2 0 1
.35 0 1
end

If I want to have the two treatment arms in the same regression, as they are define (whether they participated or not in the treatment), I estimated the ITT by:

reg exp treatment_1 treatment_2, cluster(village)

My question then is, do I need to include a variable for control group? could both treatment variables be in the same regression with cross sectional data?

Thank you

[Roman Mostazir]

The model depends on what is your hypothesis. If you are comparing whether extension+fertilizer(treatment_2) has a greater probability to use fertilizer compared to extension only (treatment_1), then you can create a variable 'group' and fit that in the OLS regression. The group difference (coefficient) in the model will test whether the difference is significantly different from `zero'. Here treatment_1 is your control group and treatment_2 is your experimental group you are comparing.

input float(exp treatment_1 treatment_2)
  1 1 0
 .6 1 0
.25 1 0
 .5 0 1
 .5 0 1
.95 0 1
 .2 0 1
.35 0 1
end


gen group=cond(treatment_1==1,1,2) //creat a group variable

reg exp i.group

      Source |       SS           df       MS      Number of obs   =         8
-------------+----------------------------------   F(1, 6)         =      0.26
       Model |  .025520838         1  .025520838   Prob > F        =    0.6305
    Residual |  .596666655         6  .099444443   R-squared       =    0.0410
-------------+----------------------------------   Adj R-squared   =   -0.1188
       Total |  .622187493         7  .088883928   Root MSE        =    .31535

------------------------------------------------------------------------------
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     2.group |  -.1166667   .2302977    -0.51   0.631    -.6801849    .4468515
       _cons |   .6166667   .1820663     3.39   0.015     .1711664    1.062167
------------------------------------------------------------------------------

[Margarita Espinoza]

Dear Roman,
I would like to disentangle both effects, assuming that extension has an effect, but indeed with fertilizer, its use is greater.
Using a group variable, Would I only look at the effect of treatment 2?
do you have a recommendation for a paper where they do a similar analysis?
thank you very much!

[Roman Mostazir]

This is what this model is doing i.e. estimating effects for both treatments and calculating the difference of their effect. The model coefficient represents the difference between two treatment effects. you can obtain the group means by the use of 'margins' command after 'regress':

margins i.group

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       group |
          1  |   .6166667   .1820663     3.39   0.015     .1711664    1.062167
          2  |         .5    .141028     3.55   0.012      .154917     .845083
------------------------------------------------------------------------------

The difference which is presented in the model output #4

margins, dydx(group)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     2.group |  -.1166667   .2302977    -0.51   0.631    -.6801849    .4468515
------------------------------------------------------------------------------

Google analysis of RCT or something similar. You should get plenty of references. Read Stata manuals for Regression, margins, etc. for understanding better. In fact, for a quick understanding, Stata manuals may help you understanding better than even some books. They are really good.

[Margarita Espinoza]

Dear Roman,
It is clear now. Thank you for the advice.
All the best