# How to calculate StdErr for intercepts and slopes in a multivariate ANCOVA (function ANOVAN() with continuous independent variable)?

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Alex Sabrekov 2022 年 1 月 4 日
コメント済み: Alex Sabrekov 2022 年 1 月 7 日
I am trying to do multivariate analysis of covariance (mANCOVA) with Matlab. There is a special GUI for it called aoctool(), but it works only for one categorial independent variable (CIV) and one covariate. So if I have two CIVs and/or two covariates, I need something else.
Fortunately, anovan() tool, initially made for n-way ANOVA, could deal with continuos independent variables. So it is possible to perform mANCOVA using this tool and it really works! One can make and tests hypothesis on variance of slopes and treatments, but to provide a comperehensive analysis one needs to compare individual models (slopes or intercepts) to find differenes between them. But stats structure in anovan() outputs contains only values of model coefficients (stats.coeffs) but not their StdErr, SSE etc. So one can not test hypothesis on equality of two slopes (using t-test). Strictly speaking, there are no multcompare() for slopes in mANCOVA.
Can somebody give me an advice (or just any help), how I can borrow data on slopes StdErr or SSE from anovan() with continuous independent variable?
Thanks, Alex.

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### 採用された回答

Jeff Miller 2022 年 1 月 5 日
If you set up dummy variables to code your categorical independent variables, you can then do analysis of covariance with fitlm. The advance of that is that you can then use regression techniques to get standard errors and confidence intervals for the model coefficients. Maybe there is an easier way, though.
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Alex Sabrekov 2022 年 1 月 7 日
As I understand, this rank deficiency is a universal and obligate property of certain linear model formulations, and it doesn't really influence on slope estimates.
Thanks again for the idea of dummy variables! I have heard with half an ear about it, but thought that it is too complicated for me. But now I realize that this is the only way to solve these problems properly. Using fitlm() also gives one an ability to estimate model with a certain confidence interval, that is necesarry for result's reporting. So there is no need to search a new tricky software.

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