How to determine/find the "ideal design sample space" in the Doehlert Experimental Design?

22 September 2023 1 10K Report

When validating the Doehlert Matrix Design, do we encounter the issue of the "ideal sample design space"? I mean, in designs like the Central Composite Design (CCD), validation is usually compromised when we choose levels between "alpha and 1", instead of selecting between +1 and -1 (the ideal design space). In the context of the Doehlert matrix, how can we ascertain/identify the ideal design space and determine if it exists?

By the way, I using 3 factors with factor 1 (5 levels), factor 2 (7 levels), and factor (3 levels)

In coded values:

Factor 1: -1, -0.5, 0, 0.5, 1

Factor 2: -0.866, -0.577, -0.289, 0, 0.289, 0.577, 0.866

Factor 3: -0.877, 0, 0.877

The question is, do the -1 and +1 in CCD correspond to the -1 and +1 in Doehlert? What ensures the curvature of the model in the case of Doehlert? This is because, according to the encoded values, all of them are between -1 and +1.

Lemya Bentrcia

Rejoignez l'alpha

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Define Same Conceptual Factors

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https://www.researchgate.net/post/How_can_I_clearly_define_factors_that_are_conceptually_the_same?pli=1&loginT=41lPzmLUjWZA5mqZPp1Tm8dihJJZB5kw7w6RfzpcnbILa_gL5DcSHID3p99d3tnPEiYUvv_np1uNW1KdZmw0yBXDU_aC&uid=qYOW8zyUx3zRaKQ7EQrjutc9j07C2EfauLy1&cp=re221_ft_j_e1_jp_p94&ch=reg&utm_medium=email&utm_source=researchgate&utm_campaign=re221&utm_term=re221_ft_j_e1_jp&utm_content=re221_ft_j_e1_jp_p94

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I am running an EFA on a data set with 250 observations. Factors 3 & 4 are basically the same conceptually (based on two questions: "Q12. Foods must be expensive to be of quality" & "Q17. I believe that expensive foods are good"). Standardization seems to be done properly. We also tried many different rotations. In most rotations, usually the factor based on Q17 has a small loading (usually around 0.5-0.6). Can we combine the two factors in EFA?

Also, our KMO is around 0.5. If I remove MSA values smaller than 0.5 it is significantly increased, but I have 2 factors (I was requested 4, not strictly, but I am afraid they are way too few).

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It sounds like you're facing some challenges in your exploratory factor analysis (EFA). Here are some suggestions:

Combining Factors 3 and 4: If Factors 3 and 4 are conceptually very similar and Factor 4 consistently has a small loading in different rotations, you may consider combining them into a single factor in your analysis. This can help simplify your model and make it more interpretable.

Low KMO Value: A KMO (Kaiser-Meyer-Olkin) value of around 0.5 suggests that your data might not be well-suited for factor analysis. You mentioned that removing items with MSA values smaller than 0.5 improves the KMO. This could be a valid approach to improve the factorability of your data, but keep in mind that it might reduce the number of factors you can extract.

Number of Factors: If you were initially aiming for 4 factors but your data doesn't support it, it's important to prioritize model fit and interpretability over a predetermined number of factors. You should select the number of factors that best represents your data based on various fit indices (e.g., scree plot, eigenvalues, explained variance) and the theoretical relevance of the factors.

Model Interpretation: It's crucial to ensure that the factors you extract make sense conceptually and align with your research objectives. If combining Factors 3 and 4 or reducing the number of factors results in a more interpretable solution, that might be a valid choice.

Consultation: Consider discussing your findings and challenges with a statistician or an expert in factor analysis. They can provide valuable insights and help you make informed decisions about your analysis.

Ultimately, the goal of EFA is to identify a factor structure that accurately represents your data and makes theoretical sense. Don't be overly rigid with the number of factors; prioritize the quality of your model and the interpretability of the results.

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I am seeking very fruitful answers for two of my questions when I face a meta-regression analysis as I am new to it. Is it possible to use a variable that has both positive and negative values ( percentage willingness to pay) as the dependent variable in a meta-regression analysis? And if we do not have SE estimates for each study, what is the method of using sample size for effect size calculation?

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In meta-regression analysis, you typically use a variable as the dependent variable that represents the effect size or outcome of interest across multiple studies. This variable should be continuous and numeric. While it's possible to use a variable with both positive and negative values as the dependent variable, you should ensure that it aligns with the research question and is appropriate for the analysis.

Regarding your second question about dealing with missing standard errors (SE) for each study, you can estimate the SEs using the sample size and other available statistics. Here's a common approach:

Calculate the Standard Error (SE) from the Sample Size (n) and Effect Size (ES):

If you have the sample size (n) for each study and the effect size (ES), you can calculate the SE as follows:

SE = ES / √(n)

Impute Missing SEs:

For studies where you don't have SE estimates, you can use this formula to impute the SE based on the sample size and the reported effect size.

Sensitivity Analysis:

After imputing SEs, it's essential to conduct sensitivity analyses to assess the robustness of your findings. You can examine how different imputation methods or assumptions about SEs affect your results.

Keep in mind that imputing SEs introduces some uncertainty into your meta-regression analysis, and it's crucial to acknowledge this limitation in your research. Additionally, consulting with a statistician or methodologist experienced in meta-analysis can be beneficial when dealing with missing data and conducting meta-regression analyses to ensure the appropriateness of your approach.