You probably already use an extension or two, maybe a password manager or some privacy addons. Taking the square root of the resulting estimated value of $Var(b_0 + b_4)$ will yield the estimated standard error of $b_0 + b_4$.Updated on OctoHow to create your first Chrome extensionĬhrome extensions are programs that enhance the functions of the browser in some way.
To compute the standard error of $b_0 + b_4$ (i.e., the intercept for Group 2), for example, recall that: $Var(b_0 + b_4) = Var(b_0) + Var(b_4) + 2Cov(b_0, b_4)$Įstimated values of the variances and covariance on the right-hand side of the above formula can be extracted from the $V$ matrix and plugged into the formula. Off the main diagonal, $V$ will contain the estimated covariances between pairs of these items. The estimated standard errors for $b_0$, $b_1$, $b_2$ and $b_3$ (which refer to Group 1) should be reported directly in the model summary produced by your software.įor Group_2, estimated standard errors can be derived from the estimated variance-covariance matrix $V$ of $b_0$, $b_2$, $b_3$, $b_4$, $b_5$, $b_6$ and $b_7$. Let $b_0$, $b_2$, $b_3$, $b_4$, $b_5$, $b_6$ and $b_7$ be the estimated values of the parameters corresponding to your model. In contrast, $β_2 + β_6$ denotes the starting level of the outcome variable $Y$ in Group 2 at the time of introduction of the intervention.įinally, $β_3$ represents the change in slope or trajectory of the outcome variable $Y$ in Group 1 after the introduction of the intervention until the end of the study, while $β_3 + β_7$ represents the change in slope or trajectory of the outcome variable $Y$ in Group 2 after the introduction of the intervention until the end of the study.
$β_2$ represents the starting level of the outcome variable $Y$ in Group 1 at the time of introduction of the intervention and indicates whether there was a change in the level of the outcome variable $Y$ in that group immediately following the introduction of the intervention.
On the other hand, $β_1 + β_5$ is the slope, or trajectory of the outcome variable $Y$ in Group 2 until the introduction of the intervention. $β_1$ is the slope, or trajectory of the outcome variable $Y$ in Group 1 until the introduction of the intervention. In the above, $β_0$ and $β_0 + β_4$ represent starting levels of the outcome variable $Y$ in Group 1 and Group 2, respectively. Now, all you have to do is to set the value of Z to 0 and 1, respectively, in your model.įor Group 1, setting Z to 0 yields the following model equation:įor Group 2, setting Z to 1 yields the following model equation (after rearranging the terms): The intervention alluded to below would be the introduction of Proposition 99. Then the variable Z in your model is defined as follows: Z = 1 for Group 2 and Z = 0 for Group 1.įor example, Group 2 could be California while Group 1 could be other states, as per the example used in Figure 2 in the paper. Let's assume you have two groups: Group 1 and Group 2.
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