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Thread: Multilevel analysis

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    Re: Multilevel analysis




    I actually think I understand the interaction (although it is not clear to me you can generate simple effects for cross level interaction as you can with normal interaction, that is the main effect of one variable at some level of another which is recommended for interaction).

    Some authors suggest you standardize variables before you run them in multilevel regression and some suggest you convert the variables after you run the regression. The standardized coefficient won't differ much if you do that, but the variance will a lot. I was wondering which is considered best practice, obviously authors disagree.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Plotting a regression line for each group is often recommended. However, I really want to run a multiple regression since I have control variables that need to be in the model. Is there any way to visually get at a regression space the way you would a line?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Didn't the Wang book use spaghetti plots if I remember right?
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    Re: Multilevel analysis

    You want to use maximum likelihood if you can in MultiLevel models because it allows you to use deviation to determine which model is better. But Maximum Likelihood is biased for variance parameters when the sample size is small. Specifically when N- Q-1 >= 50 the rule of thumb is it won't matter which approach you use. The problem is that while I know Q is largely the number of level 2 predictors, I am unsure what N is. I assume this means the sample size but the author who mentions it (Snijders and Bostker) do not define it (probably they assume its obvious)?

    Does anyone know what N is?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Quote Originally Posted by hlsmith View Post
    Didn't the Wang book use spaghetti plots if I remember right?
    I missed this if it occurs.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    In multilevel models with random slopes the observations are heteroscedastic because their variances depend on the explanatory variables,....However, their residuals are assumed to be homoscedastic.....In chapter 8 it was explained that the multilevel model can also represent models in which the level 1 residuals have variances depending on an explanatory variable say, X. Such a model can be specified by the technical device of giving this variable X a random slope at level 1.
    I do not understand this. Any comments would be appreciated. I do not understand if you do or do not need to check multilevel models for hetero.

    Incidently Sir Fisher should be shot for using the term heteroscedastic - one of the hardest words to spell I have run into...
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    I am really confused how you inspect the residuals in multilevel models. Some suggest inspecting them separately, that is level one and level two and some suggest looking at each level 1 separately for each group [which for me would be very time consuming since I have 30 plus groups - also I am not sure what you do if some groups show unequal error variance and others do not).

    Can you just inspect the residuals of the combined model. Similarly I do not know how you do analysis of violations of assumptions at the 2nd level for things like non-linearity.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Misspecifying the number of random effects and/or their covariance structure can also lead to biased point estimates when the outcome variable is discrete (Litière et al., 2007). Thus, when choosing to model clustered data with HLM, researchers with continuous outcomes and large sample sizes can be fairly confident that their results are robust to a misspecified covariance matrix or the exclusion of a random effect. However, with continuous outcomes with small or moderate number of clusters or with discrete outcomes, a violation of either assumption can adversely affect inference from model estimates.
    When they say large sample sizes do they mean the number of cases, or how many groups there are? I have seen both of these used to determine sample size. Is there a rule of thumb of what large is?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Interpretation of this variation is easier when we consider the standard deviation which is the square root of the variance. A useful characteristic of the standard deviation is that with normally distributed observations about 67 percent of the observations like between one standard deviation above or below the mean. See 19 for how you calculate this. But as an example if the mean is .45 and the standard deviation .18 than 67 percent of the means like between .45-.18 and .45 + .19 and 95 percent lie between .45 –(2*.18) and .45 + (2*.18). the more precise value is 1.96 rather than 2 in the example above.
    Where do you actually find this square root of the variance in the model? I am not sure what they are using. This deals with analyzing how slopes vary across groups when a random effect is present.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Just guessing, but the SEs of slopes are the stdev of the population.


    I don't know the full context you are looking at but the stdev of posterior densities (from bayes) are analogous to the standard errors from frequentist approaches.
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    Re: Multilevel analysis

    Comments on the p values for random effects say these are generally invalid with small sample sizes. We have about 70 units, our groups. Is that enough not to be small?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    Would you be happy with a sample size of 70? What is the random effects variable(s)?
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    Re: Multilevel analysis

    It is 70 groups, there are thousands of cases (but groups is the key to the sampling as I understand it not cases). I have not decided yet what the predictors will be. We have actually 92 groups, but many of these are small.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Multilevel analysis

    I think about it as a model in a model (between groups, within groups).
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    Re: Multilevel analysis


    It's strongly suggested that you not use the Wald p values for at least random effects in multilevel models (some suggest not using them for fixed effects either). Instead it is suggested you do a deviance (LR) test, testing one variable at a time (that is adding one to the model each time). II have found no guidance on what order makes the most sense. Two examples of this are below.

    When you suspect a predictor has a fixed effect, and possibly a random one as well, do you have to first test the fixed effect with a LR then the random effect?

    Do you have to test if there is a random intercept before you test if a slope is random? And if the intercept is not random, does it make sense to test for random slopes?
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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