<p>It isn't exactly clear what you are asking, it seems that you are unsure of what you should be modelling, which is a statistical question and may be more appropriate on Cross Validated, but it also seems that you are unsure about R (or rather the package <code>lme4</code>) syntax.</p>

<p>Check out this <a href="https://arxiv.org/pdf/1406.5823.pdf" rel="nofollow noreferrer">https://arxiv.org/pdf/1406.5823.pdf</a> comprehensive guide to using <code>lme4</code>, specifically page 6 will be helpful for understanding random effects syntax. From that document: </p>

<p><em>"Each random-effects term is of the form (expr|factor). The expression expr is evaluated as
a linear model formula, producing a model matrix following the same rules used in standard
R modelling functions (e.g., lm or glm). The expression factor is evaluated as an R factor"</em></p>

<p>When you have RE terms specified like this: <code>(1|participant) + (1|pre_post)</code> that means that the RE are crossed (see PeerJ paper below), whereas <code>pre_post + (1+ pre_post|participant)</code> is a correlated intercept and slope (see page 6 in link above).</p>

<p>I agree with @sjp that you don't want to use a random effect for something with only two levels. This paper, which is a wonderful introduction to mixed models, suggests that you should have at least 5 levels: <a href="https://peerj.com/articles/4794/" rel="nofollow noreferrer">https://peerj.com/articles/4794/</a> </p>

<p>An alternative to @sjp suggestion of log transforming data that might work for trial time data is to use the <code>glmer()</code> function with a <code>family=gamma</code> argument, but either way it is good to inspect residual plots for model fits <a href="http://www.sthda.com/english/articles/39-regression-model-diagnostics/161-linear-regression-assumptions-and-diagnostics-in-r-essentials/" rel="nofollow noreferrer">http://www.sthda.com/english/articles/39-regression-model-diagnostics/161-linear-regression-assumptions-and-diagnostics-in-r-essentials/</a>. </p>

<p>In the case that you don't actually need a random effects term, then the base R functions <code>lm</code> and <code>glm</code> will replace <code>lmer</code> and <code>glmer</code> respectively.</p>
mixed models design and syntax in R
<p>I am new to mixed model analysis. Can somebody help me to get things clear? </p>

<p>I have the follwoing repeated measurement design: 
<em>pre test - intervention - post test.</em> </p>

<p>Varaibles: 
<strong>Go_rt</strong> - reaction time. 
<strong>pre_post</strong> - categorical variable (pre-test;post-test)
<strong>expectation</strong> - participants expectations. </p>

<p>I have the follwoing R code where I want apply mixed model to evalute wether reaction time is statistically different (pre-test vs post test). Plus I want to whether there is interction with effect with participants expectations. </p>

<p><em>mod &lt;- lmer(Go_rt ~ pre_post +expectations + pre_post:expectations + (1|participant), data=data,
          REML=FALSE)</em></p>

<p>What I doubt about is whether the pre_post variable has to be specified in the random part. So the code will look like this: </p>

<p><em>mod1 &lt;- lmer(Go_rt ~ pre_post +expectations + pre_post:expectations + (1+ pre_post|participant), data=data,
          REML=FALSE)</em></p>

<p>And what will it change if I change it like this? </p>

<p><em>mod2 &lt;- lmer(Go_rt ~ pre_post +expectations + pre_post:expectations + (1|participant) + (1|pre_post), data=data,
          REML=FALSE)</em></p>

<p>Actually the mod2 give me significant results for interaciton effect whereas mod &amp; mod1 does not. </p>