Help -Inference about interaction coefficients in two-factor study

The model includes factors such as the gene, the presence of the disease, and an interaction between the two. The speaker is unsure of how to test a specific hypothesis regarding one gene's connection to the disease. The expert suggests creating a dummy variable for that gene and interacting it with the disease to test the hypothesis. In summary, the conversation discusses a model for analyzing the relationship between a gene and a disease, and the expert suggests using a dummy variable and interaction to test a specific hypothesis.
  • #1
solar42
2
0
I have measurements of some response of a gene, and two factors: the gene, g=1...G and whether the patient/subject has a certain disease, t=1,2.

the full model is
[tex]
y_{gtk}=\mu+\alpha_g+\beta_t +(\alpha\beta)_{gt}+\epsilon_{gtk}

[/tex]

I know that to see if genes have any connection at all with the disease, I just fit the reduced model without the [tex] (\alpha\beta)_{gt} [/tex] interaction and compare the two, but if I want to see if, say, gene number g=25 has anything to do with the disease... I know that the null hypothesis is [tex] H_0 : (\alpha\beta)_{25,t}=0, \textrm{ for all } t[/tex], but how do I test this hypothesis? I am confused at what to do when I can't drop the whole factor and compare.
 
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  • #2
You can define a separate "dummy" variable for gene 25 and interact it with the disease.

EnumaElish
 
Last edited:

1. What is a two-factor study?

A two-factor study is a type of experimental design where two independent variables, also known as factors, are manipulated to observe their effects on a dependent variable. This allows researchers to study the interactions between the two factors and their impact on the outcome of interest.

2. Why is inference about interaction coefficients important in a two-factor study?

Inference about interaction coefficients allows researchers to determine if the effects of two factors on a dependent variable are dependent on each other or if they act independently. This information is crucial in understanding the relationship between the variables being studied and can provide insights into how they influence each other.

3. How are interaction coefficients calculated in a two-factor study?

Interaction coefficients are calculated using statistical analysis, such as ANOVA or regression, to determine the magnitude and significance of the interaction effect between the two factors. This involves comparing the variation in the dependent variable explained by the interaction term to the variation explained by the individual factors.

4. What does a significant interaction coefficient indicate in a two-factor study?

A significant interaction coefficient indicates that the effect of one factor on the dependent variable is different at different levels of the other factor. In other words, the two factors are interacting and their combined effect on the outcome is not equal to the sum of their individual effects.

5. What are some limitations of inferring about interaction coefficients in a two-factor study?

One limitation is that interaction effects can only be inferred from the specific levels of the factors that were included in the study. This means that the results may not be generalizable to other levels or combinations of the factors. Additionally, it is important to consider the sample size and potential confounding variables that may influence the interaction effect.

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