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How to write down GLM formula with a 2x2 within-between experimental design(如何写出具有2x2内试验设计的GLM公式)

转载 作者：bug小助手 更新时间：2023-10-25 12:05:17 26 4
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I have conducted a research in which the experimental design is 2x2.

我进行了一项研究，其中的实验设计是2x2。


I have a independent variable called strum which is a two-level factor and is within participants (so same participants in two different times). Then I have another independent variable called cond which is also a two-level factor and is instead treated as a between-subjects variable (so two different groups).
I would like to apply a lmer and a glm or glmer formula to fit the model and then apply an Anova, considering also the interaction effect. How can I write down the formula? How would be the syntax of it?

我有一个名为strum的自变量，它是一个两级因素，在参与者中(所以相同的参与者在两个不同的时间)。然后我有另一个自变量，叫做cond，它也是一个两级因子，而不是被视为受试者之间的变量(所以是两个不同的组)。我想应用LMER和GLM或GLMER公式来拟合模型，然后应用方差分析，同时考虑到相互作用的影响。我怎么才能写下公式呢？它的语法会是怎样的？


I tried with this formula:

我试着用这个公式：


minv=lmer(pqinvolv~(strum*cond|pqinvolv)+(strum|id), data=dv_n)

where pqinvolv is the dependent variable, but it gives me an error

其中，pqinventv是因变量，但它给了我一个错误


and also this one:

还有这一张：


minv=lmer(pqinvolv~strum*cond+(1|id), data=dv_n)

while this one works, but I'm not sure it consider my IV as a mixed model or just a two way repeated measure with all the variables being measured as within-subjects.

虽然这个方法有效，但我不确定它是否认为我的IV是一个混合模型，或者只是一个双向重复测量，所有变量都作为受试者内部测量。


更多回答

Can you edit your question to include the error message you get?

您可以编辑您的问题以包括您收到的错误消息吗？

优秀答案推荐

Based on your description,

根据你的描述，


pqinvolv ~ strum*cond + (1 + strum|id)

would be an appropriate model: strum*cond (which expands to 1 + strum + cond + strum:cond) specifies the main effects of strum and cond and their interaction at the population level, while 1 + strum|id allows the effect of strum to vary among participants. You can't include cond in the random effect because it's unidentifiable (i.e., since it's a between-subjects factor, you can't tell how its effect varies between subjects). (I can't think of any scenario where putting the dependent variable (pqinvolv) anywhere on the right side of the formula makes sense.)

将是一个合适的模型：strum*cond(扩展为1+strum+cond+strum：cond)指定strum和cond的主要效果以及它们在种群水平上的交互作用，而1+strum|id允许strum的效果因参与者而异。你不能在随机效果中包含cond，因为它是不可识别的(即，因为它是主体间的因素，你不能知道它的效果在不同主体之间有什么不同)。(我想不出有什么场景可以将因变量(Pqinventv)放在公式右侧的任何位置。)


However, since you only have two levels of strum, the among-subject variation in strum effect is confounded with the residual variance, so you should simplify your model to

但是，由于您只有两个级别的strum，所以strum效果中的主体间差异与残差方差混淆，因此您应该简化您的模型以


pqinvolv ~ strum*cond + (1|id)

(This assumes you are fitting a linear mixed model, not a generalized linear mixed model with a fixed scale parameter, e.g. for Poisson or binomial responses.)

(这假设您拟合的是线性混合模型，而不是具有固定比例参数的广义线性混合模型，例如泊松或二项响应。)


A similar situation is described in the "starling example" here.

类似的情况在这里的《八哥范例》中也有描述。


更多回答

I'm very thankful for your reply and you tryina helping me. I have tried with the formula you wrote down, but once I run it, ti gives me this kind of error: Error: number of observations (=96) <= number of random effects (=96) for term (1 + strum | id); the random-effects parameters and the residual variance (or scale parameter) are probably unidentifiable Which I think is a matter of observation since strum is as factor with 2 levels cond is as factor with 2 levels id is as factor with 48 levels. the total amount of obs are 96, which meant there were 48 participants

我非常感谢你的回复和你试图帮助我。我试过你写下的公式，但一旦我运行它，ti给我这样的错误：Error：观察次数(=96)<=项(1+strum|id)的随机效果数(=96)；随机效果参数和残差方差(或比例参数)可能无法识别，我认为这是观察的问题，因为strum是2级条件的因素，id是48水平的因素。OB的总数为96个，这意味着有48个参与者

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