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Thanks for the feedback! So first of all, the LMM is perfectly capable of dealing with missing data (unlike RM ANOVA). Why not try just running the analysis with the data points missing? Some would argue that imputing missing data points can lead to severe bias. If you are dead set on estimating these values, one solution is to calculate a mean of your 20 imputations for each missing data point and then to use that value to "fill in" the data set.

@@tonycarlsen1627 , thank for your immediate response. In our team we tend to impute missing data to avoid any bias due to them. About calculating a mean from imputed datasets - I am not sure, but I hard that 'combined' data in SPSS is something different than just 'a mean score from imputation'. Am I right, or not? Additional question - I also have JASP - is it possible to estimate missing data and conduct LMM there? I saw your tips to conduct LMM in JASP in the video, but I wonder how it looks with missing data.

@@niziolek933 Yes, you can use JASP as shown in the video although I'm pretty sure JASP will not do any imputation, but again, I'd try it using your data set with missing data. On another note, I'm unsure how making up (imputing) data points can lead to *less* bias... my opinion is that you should model your data as they are, not some idealized version of them. Hope that helps

Hey - thanks for the great question! In the summary() of the model, the coefficients and associated p-values represent the individual slope with respect to the "reference category" when the predictors are categorical variables as they are here. So here, R has specified [Female, Informal] as the reference category, so the slope for sexMale =116.195 (p = .00376) is just the slope between [Female, Informal] and [Male, Informal] (by the way, the slope is simply the difference between the means in this example). The same thing applies for attitude polite. This slope is simply the difference between the reference category [Female, Informal] and [Female, Polite]. For the anova() output, it examines the "overall" effect of sex (or attitude) across both levels of the other variable. For example, the effect of attitude is calculated across both sexes, so the effect is different. You can imagine that the effect of attitude is not exactly the same for males as it is for females (if it were, the interaction effect would be p = 1.0). Here is is not "significant" but that does not mean the effect is the same for both sexes either, so the p-values for the individual effect of attitude for females (p=.0031) is different than the effect of attitude across both sexes (p=.0034). Hope that helps clarify

@@tonycarlsen1627 Thank you so much for the detailed information! That solved me a long lasting confusion... And may I ask for another question. Someone recommends to use Anova in "car" package over the anova command in base package. I myself ran those two commands on the output of lmer, and got different P values. So do you have any idea on the difference between these two? Many thanks again.

Hi Melanie - great question, and this is often a bit misunderstood. The Test of fixed effects shows that the overall effect of attitude in the model is significant p = .003. This means that when looking at this factor collapsed across the other factors (sex) the effect is significant. The estimates of fixed effects is giving you a specific comparison. Here it is asking "is the effect of informal attitude different as compared to the reference category (i.e. intercept)?". Here the reference category is Male-polite, so it is comparing male-informal to that category, which as a specific comparison, is not significantly different. Hope that helps!

Hi Süleyman, I believe that you would have to use the SPSS scripting functions to apply a random slope in SPSS. See the following tutorial which demonstrates how these are specified in the syntax: www.theanalysisfactor.com/spss-genlinmixed/

Hi Simone, the LME does not calculate SD for the EMM; instead, because of the way the variables are calculated standard error is provided (and 95% CI). Indeed, because there can be multiple random effects, the SD's become less meaningful... see a similar question/response here: www.researchgate.net/post/Looking-for-a-way-to-derive-standard-deviations-from-estimated-marginal-means-using-mixed-linear-models-with-SPSS

​@@tonycarlsen1627and @MomoSimone22 Thank you for asking/answering this question. I have a few follow-up questions: 1. In the case that SDs become less meaningful and are not generated in the emmeans output from a linear mixed effect model, would you recommend simply using the estimated marginal means and SEs when reporting results? Even if this approach is acceptable, oftentimes the SEs are the same or very similar, and do not look good when creating a descriptive table that includes estimated marginal means and SEs of the dependent variable by each of the factors included in the model. 2. I have seen some papers taking a different approach to create the descriptive table by reporting the true means and SD calculated by the raw data. This sometimes cause issues because in some cases (i.e., random effect included in the model, missing observation from the dataset), the estimated marginal means and the true means (calculated using the raw data) are different. In the worst, statistically there can be a significant difference (and apparent numerical difference) between two estimated marginal means based on the emmeans output, but the numerical difference between the two true means (calculated by the raw data) are very small. Thus, reporting the true means/SDs would make the results very strange. If this happens, should I report both the estimated marginal means/SEs and true means/SDs, and explain why they are different? Or simply ignoring the true means/SDs to avoid confusion? Thank you very much for your time in advance! Alvin

If lme4 is not (currently) compatible with the latest version of R, you can install a previous version of R (e.g. 4.1.3) alongside your current one (just visit r-project.org), and then select the version of R you want to use in RStudio by going to Tools > Global Options > General > R Version, and selecting the "change" button. Hope that helps!

@@tonycarlsen1627 The incompatible is really annoying! Thank you for your suggest, I will try that!

Hey Cyberklutz - my understanding is that traditional split-half reliability estimation is no longer considered the best measure of internal consistency due to several limitations. However, Chronbach's alpha may be a better approach to use. A JASP tutorial can be found here: ruclips.net/video/dMdv4Ro9GrQ/видео.html

@@tonycarlsen1627 Thanks. Much appreciated.

I think what you may be looking for is the VarCorr function. see rdrr.io/cran/lme4/man/VarCorr.html

@@tonycarlsen1627 thanks man, This for the mixed-effects too or only fixed-effects? I didn´t understand this part.

Hey Emily, I just came from another video that (if I understand correctly) explains that Linear Mixed Models takes care of the violation of independence (that it is, observations are not independent and therefore could be correlated). So you should be okay to run the analysis if your observations aren't independent. For example, comparing the same participants in two experimental conditions. If your variables are correlated, that seems to be okay. ruclips.net/video/c_tYZxQLoDA/видео.html

Hi Aline, Yes - that is certainly one way of following up a significant interaction effect. What you are referring to is called "simple main effects" analysis. It is typically used if you have a specific a-priori hypothesis regarding one of the treatment levels. You would then follow up the (Bonferroni or otherwise corrected) simple ANOVA with pairwise post-hoc tests. Depending on how it is done, this can be a *less* conservative method, as in the end, the follow-up post-hoc tests would be correcting for fewer comparisons. For example if you had 2 groups (one control and one intervention) and measured them at four times and found an interaction, you could then do two 1-way ANOVAs on each of the group using a corrected p-value of .025 (assuming that your intervention predicts that one group would change and the control group would not). After that you could follow up the significant ANOVA with corrected pairwise comparisons among the four times, needing a Bonferroni corrected p-value for 4 means (or 6 comparisons) of .0083 . Note, that if you then also follow up the between group differences at each time with uncorrected independent t-tests, then you are inflating your type I error rate. The way I've outlined the follow up tests is if you want to determine post-hoc where any differences lie. This is arguably a more conservative method and requires fewer steps. It corrects for *all* possible pairwise comparisons at once (in this case it would be 8 means, or 28 potential pairwise comparisons). Because a Bonferroni correction can be too conservative with more than ~6 comparisons, we then often choose a less conservative post-hoc correction procedure such as Tukey's HSD or Holm-Bonferroni. In the end the analysis method you choose depends on your hypothesis(es), and you just need to justify it appropriately.

@@tonycarlsen1627 Thank you so much!!

The assumption of normality in Linear Mixed Models relates to the distribution of the *residuals*. So to do this in SPSS, you need to click on "Save" in the analysis dialog (see this in the video at 3:30 just under EM Means box). A new dialog box will come up where the last option at the bottom is "Residuals." Select the check box. Once you run your analysis, you will have a new column of data which are the residuals, which you can then do test of normality on (or plot a histogram of, etc.). You can also select "Predicted values" in the same dialog box, which you can use to plot the predicted values vs. residuals to examine heteroscedasticity, the same way you can in R (see video at 21:57). In terms of reporting, the type III tests of fixed effects would be more akin to what would typically be reported in a mixed ANOVA, so people familiar with normal mixed ANOVA would understand. In contrast, the estimates of fixed effects is more similar to what would typically be reported in a multiple regression. That is, they provide an estimate of what each factor adds to the slope of the model, and whether it is significant. Hope that is all reasonably clear.

@@tonycarlsen1627 Thank you so much Tony.. that was very clear and much helpful 😊 One question regarding the normality test. If I have for example 2 intervention groups and 2 measuring points (time 1, 2), do I need to test normality of resd. for both groups at each time point? Or would it be sufficient to test normality of residuals with intervention groups only?

​@@monaadnan3829 The residuals for the full model are what you test. That is, when doing the model with 2 fixed factors (intervention and time), each with 2 levels, you get a single set of residuals. You could run the models on each factor alone and then test the residuals of each, but in your situation I'm not sure that is very helpful.

Hi Patrice, see this link for running JASP in a browser: jasp-stats.org/2018/05/01/how-to-run-jasp-in-your-browser/

No, but you can use the glmer command (generalized linear mixed effects) from the lme4 package in R to do this, but you will also need to add "family = binomial" to the command. See stats.idre.ucla.edu/r/dae/mixed-effects-logistic-regression/ for more info, or simply do a search for "glmer logistic regression" to see other examples.

@@tonycarlsen1627 thanks a lot. Can You also pls tell why in jasp it Doesn't show random effect and r it shows. How to explain the variance in random effect?

@@mollikaroy7424 My understanding is that the variance of the random factor ("subject" in our example) tells you how much variability there is between individuals (or whatever the random effect is) across all treatments. Often we don't care much about individual differences except to model them appropriately, so my guess is that is why JASP does not provide them as an output. Fore more see www.r-bloggers.com/2012/11/making-sense-of-random-effects/