{"id":282,"date":"2015-07-01T13:13:37","date_gmt":"2015-07-01T18:13:37","guid":{"rendered":"http:\/\/justinwiegand.com\/blog\/?p=282"},"modified":"2026-03-10T22:30:38","modified_gmt":"2026-03-11T05:30:38","slug":"using-polynomial-regression-pr-and-response-surface-methodology-rsm-to-determine-effects-of-fitcongruence","status":"publish","type":"post","link":"https:\/\/justinwiegand.com\/blog\/?p=282","title":{"rendered":"Using Polynomial Regression (PR) and Response Surface Methodology (RSM) to Determine Fit\/Congruence"},"content":{"rendered":"

A prominent research interest of mine is\u00a0assessing person-vocation fit and its relationship to\u00a0work outcomes, such as job performance. \u00a0Polynomial regression (PR) and response surface methodology (RSM) are ideal methods for\u00a0measuring person-vocation. \u00a0Reasons for the superiority of PR-RSM are numerous, but not the point of this post. \u00a0The interested reader should see Jeff Edward’s writings\u00a0here<\/a>\u00a0and here<\/a>\u00a0for rationale. \u00a0The point\u00a0of this post is to offer high-level, practical guidance on how to apply PR-RSM to fit questions. \u00a0So, without further ado:<\/p>\n

PR-RSM Guide for Evaluating\u00a0PE Fit<\/p>\n

    \n
  1. Have \u00a0a useable data set. Finding higher-order effects (i.e. effects for squared and interaction terms) generally requires larger samples for adequate power.<\/li>\n
  2. Have an interesting research question–have (theoretically-grounded) fun with this. \u00a0The reality is that polynomial regression allows you to do much more than assess congruence and incongruence broadly. \u00a0Rather, you can hypothesize\u00a0about incongruence at low, mid, or high levels of scale strength. \u00a0For example, at mid-levels, you can think about incongruence when one component (person or environment) is higher or lower than the other (evaluated by the line of incongruence). \u00a0You can hypothesize about changes along the line of congruence as well (e.g., is an outcome higher when congruence between components is high-high compared to low-low?).\n
      \n
    1. More specifically, I recommend considering the following areas of the plot for hypothesis development:\n
        \n
      1. First, consider\u00a0the congruence line.\n
          \n
        1. Should the outcome of interest change along the congruence line?<\/li>\n<\/ol>\n<\/li>\n
        2. Next, consider\u00a0where the outcome\u00a0should be\u00a0highest.\n
            \n
          1. Is it somewhere along the congruence line (i.e. supporting P-E Fit), or is it somewhere representing a degree of incongruence?<\/li>\n
          2. If the outcome is highest where incongruence exists,\u00a0develop theoretical reasons for this.<\/li>\n<\/ol>\n<\/li>\n
          3. Next, discuss incongruence when your referent variable (e.g. the “person-side” in person-vocation fit) is\u00a0low (vocation\u00a0high), medium (vocation high and low), and high (vocation\u00a0low).<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n
          4. Add relevant controls and fix them at their average when plotting the response surface plot.<\/li>\n
          5. Use F-tests to see if your addition of fit-related variables from linear to quadratic (including the interaction term) is significant. \u00a0You will ultimately\u00a0interpret the response surface, so you are most interested in whether the additional terms add a significant change to your existing model and not whether the coefficients are significant individually. \u00a0SAS and Systat will both compute these F-tests for you when doing their respective PR functions (Proc RSREG and RSM respectively). I also have syntax to do this in R. \u00a0Notably, Systat and SAS both separate the addition of squared terms from the addition of an interaction term, so to compare these added together at the same time requires additional model comparisons.<\/li>\n
          6. Plot your results. SAS’s RSREG procedure allows this as does Systat’s RSM. \u00a0Systat can plot a linear or quadratic surface while the RSREG procedure in SAS will not plot linear graphs! In R, I highly recommend the RSM package for plotting and analysis. \u00a0Also note, that while you can easily rotate the plot in SAS’s RSREG procedure via a “rotate=xx” option (a similar option exists in the R RSM syntax), SYSTAT and the RSM package both offer a “mouse click\/hold and rotate” option which is really helpful for quickly viewing the plot from multiple angles. Whichever program you use, be consistent as it will be hard to\u00a0format plots to look the same using the two different programs. \u00a0Jeff Edwards also provides an Excel spreadsheet to create surface plots<\/a> (for SPSS users, you can directly enter output into the spreadsheet).<\/li>\n
          7. Now interpret the results in line with your hypothesized relationships (developed in point “2” above). \u00a0It may be helpful to create a table of hypothesized conditions and note when each is or is not met across all analyses (as in Edwards & Cable, 2009). \u00a0You should also show regression coefficients and the results of your significance tests for adding both the linear and quadratic terms of interest for each\u00a0surface plot. \u00a0Show the relevant surface plot and report hypothesized aspects of the plot for significance (i.e. the slope and curvature of the line of congruence). \u00a0See Edwards (2002) and Edwards and Parry (1993) for direction on significance tests of response surface characteristics.<\/li>\n<\/ol>\n

            I hope this helps motivate those with interesting fit questions to think about using PR and RSM. \u00a0This has largely been aimed at examining hypothesized relationships, but you are free to do exploratory analysis as well. \u00a0There are challenges to accomplishing the necessary analysis and\u00a0interpreting 3D plots, but the method is well worth the effort!<\/p>\n

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            A prominent research interest of mine is\u00a0assessing person-vocation fit and its relationship to\u00a0work outcomes, such as job performance. \u00a0Polynomial regression (PR) and response surface methodology (RSM) are ideal methods for\u00a0measuring person-vocation. \u00a0Reasons for the superiority of PR-RSM are numerous, but not the point of this post. \u00a0The interested reader should...<\/p>\n","protected":false},"author":1,"featured_media":283,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"Using Polynomial Regression (PR) and Response Surface Methodology (RSM) to Determine Effects of Fit\/Congruence http:\/\/wp.me\/p51adQ-4y","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[4,79],"tags":[84,82,83,59,81,80],"class_list":["post-282","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-methods","category-polynomial-regression-response-surface-methodology","tag-pe-fit","tag-polynomial-regression","tag-response-surface-methodology","tag-sas","tag-spss","tag-systat"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/justinwiegand.com\/blog\/wp-content\/uploads\/2015\/07\/PNregExample.png?fit=1333%2C1000&ssl=1","jetpack_shortlink":"https:\/\/wp.me\/p51adQ-4y","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=282"}],"version-history":[{"count":15,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/282\/revisions"}],"predecessor-version":[{"id":892,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/282\/revisions\/892"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=\/wp\/v2\/media\/283"}],"wp:attachment":[{"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/justinwiegand.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}