I am conducting a study which has 3 IVs ( POP, SOE, PI) and 1 DV (COO). 2 of the IVs (POP and SOE) are manipulated variables for high/ low, making 4 groups. However, the third IV (PI) is a measured variable which is a continuous variable. This means i cannot manipulate it to create high/ low conditions.
Should i convert the continuous IV (PI) to high/low conditions to make a 2x2x2 design?
If yes, what values of the high/ low aspects will i enter into my data sheet ?
If no, what options do i have for my analysis?
Someone told me it is not a good idea to convert the continuous third IV to a categorical variable. They told me the options i have are either Hierarchical regresison analysis or multiple regression analysis with interaction terms.
I would like to mention that i would also like to see the interactive effects of all three IVs, not only combinations of 2 IVs, on the DV. I want to hypothesize that COO will be highest for the combinations of High POP, high SOE, and high PI. Alternatively, the COO outcome should vary for high PI, when POP and SOE are high.
I would like suggestions to gain clarity on the best apporach i should follow, and the tests my study needs. For any analysis, what values do i enter in my data sheet for high/ low values of the two categorical IVs?
Sundas Azim, In your study with three independent variables (IVs) and one dependent variable (DV), it's generally not recommended to convert a continuous IV like PI into a categorical variable, as doing so can lead to a loss of information and statistical power. Instead, you can employ hierarchical regression analysis or multiple regression analysis with interaction terms to examine the interactive effects of all three IVs on the DV. To investigate your hypothesis that COO will be highest for the combination of High POP, high SOE, and high PI, you can create interaction terms for these conditions and include them in your regression model. For instance, you can create a variable that multiplies the values of POP, SOE, and PI when they are all high. Similarly, you can create interaction terms for other combinations you want to explore. This approach allows you to assess the impact of each IV while considering their interactive effects, avoiding the need to categorize the continuous variable PI. In your data sheet, you would enter the actual continuous values for POP and SOE, and for PI, you would enter the measured values. Ensure you center your continuous IVs (subtract the mean from each score) to aid in the interpretation of interaction effects. This approach will provide a more robust and informative analysis for your research question.
As Engr. Tufail noted, carving quantitative variables into categories prior to analysis can cause many problems. Here is a summary you might find useful:
- https://discourse.datamethods.org/t/categorizing-continuous-variables/3402
See: https://www.researchgate.net/post/Is_it_possible_to_test_variation_in_a_DV_for_2x2x2_design_for_2_manipulated_and_1_measured_variable
Others have provided useful guides. In addition, I'm thinking you could perform a Latent Class A Analysis on the PI to see how many categories or groups will emerge. Thereafter, use the group membership (that will emerge after the analysis) for your main work. The LCA is one of the contemporary approaches to convert such continuous data into categorical.
@Tufail Mabood thank you for your answer. However, you mention that I should enter continuous variable values for POP and SOE. These are categorical manipulated high/ low variables not continuous.
Also, should I add 0 and 1 for low and high values for both variables? If so, interaction terms including zero for any "low" category for the two variables would give 0. Is that fine?
Engr. Tufail , Valentine Joseph Owan , Bruce Weaver , Sal Mangiafico Thank you all for your help.
Could you also help me understand that would i simply enter 1s and 0s for high and low values for both POP and SOE ? For statisticall analysis does this suffice to reflect the effect of the vignettes that i created?
Furthermore, for interaction terms, for low/ low groups, i am likely to get 0. Is this likely to adversely affect my analysis?
There are many ways to code dichotomous (and categorical) variables, but dummy (or indicator) variable coding (0/1) is one common way. So yes, you can do that. And the fact that some of the product terms will be 0 is nothing to worry about. To understand the nature of any interactions you detect, plot fitted values of Y at relevant combinations of the explanatory variables. Do a search on to find examples. If you say what software you use, readers may be able to direct you examples using that software. HTH.
PS- Some of the responses and links shown here may be useful.
https://stats.stackexchange.com/questions/295134/binary-and-continuous-variables-in-the-same-regression
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