{"id":4284,"date":"2018-09-18T18:50:30","date_gmt":"2018-09-18T22:50:30","guid":{"rendered":"https:\/\/www.amyork.ca\/academic\/zz\/?p=4284"},"modified":"2018-09-18T18:57:50","modified_gmt":"2018-09-18T22:57:50","slug":"factorial-validity","status":"publish","type":"post","link":"https:\/\/www.amyork.ca\/academic\/zz\/psychological-measurement\/factorial-validity\/","title":{"rendered":"Factorial validity"},"content":{"rendered":"<ul>\n<li>Is relevant to determining whether the scores of a measure correspond to the number and nature of dimensions of theorised dimensions that underlie the construct of interest<\/li>\n<li>Researchers use a data technique known as factor analysis to help determine the number and nature of dimensions associated with the scores derived from a test<\/li>\n<\/ul>\n<p><strong>Factorial validity:<\/strong><\/p>\n<ul>\n<li>Pertains to the <u>internal structures<\/u> of test scores<\/li>\n<li>A tests internal structure is the way that parts of the test are related to each other<\/li>\n<li>The actual (empirical) structure of the test should match the theoretical or intended structure of the test<\/li>\n<li>In a very simplistic sense, factorial validity helps specify what the test measures<\/li>\n<li>That is, with respect to the<u> number<\/u> of dimensions, and the <u>definition<\/u> of those dimensions<\/li>\n<li>The definitions of the dimensions are determined by which items <u>\u2018load\u2019<\/u> onto which dimension<\/li>\n<li>To determine the number of dimensions that underlie an inventory, as well as their definitions, we (can) use a data analytic technique known as factor analysis <strong>o <\/strong>Helps us clarify the number of factors within a set of terms<\/li>\n<\/ul>\n<p><strong>o <\/strong>Helps us determine the which items are linked to which factor, which facilitates the interpretation of those factors<\/p>\n<p><strong>Measurement:<\/strong><\/p>\n<ul>\n<li>Typically, when we attempt to measure an attribute, we try to do so in such a way that the score represents a single attribute<\/li>\n<li>g. based on six item questions (3 on social interaction, 3 on intellect), if the total was calculated, what would that composite score mean?\n<ul>\n<li>It would be a compromised score, because the items do not all measure the same dimension<\/li>\n<li>We try to avoid these situations, want composite scores that are \u2018factor pure\u2019<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Dimensionality:<\/strong><\/p>\n<ul>\n<li>Generally, three types of tests:<\/li>\n<li>Unidimensional test o Consists of items which all measure one, single factor<\/li>\n<li>Multidimensional test (uncorrelated)<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>o Consists of items which measure two or more dimensions which are unrelated to each other<\/p>\n<ul>\n<li>Multidimensional test (correlated) o Consists of items which measure two or more dimensions which are correlated with each other (positively or negatively)<\/li>\n<\/ul>\n<p><strong>Unidimensional tests:<\/strong><\/p>\n<ul>\n<li>Include items that reflect only a single attribute<\/li>\n<li>The items are not affected by other attributes<\/li>\n<li>Consider a multi choice exam, students get one score on the final exam (presumes the test is also Unidimensional\/justifiable to yield one score)<\/li>\n<\/ul>\n<p><strong>Multidimensional test:<\/strong><\/p>\n<ul>\n<li>This is a model of a correlated multidimensional test<\/li>\n<li>Each item is linked to one attribute only, but there are there are two distinct attributes which are correlated with each other<\/li>\n<li>This is a model of an uncorrelated multidimensional test, each items is linked to one attribute only.<\/li>\n<\/ul>\n<p>o There is no link between the two dimensions<\/p>\n<p><strong>Implications of factorial validity:<\/strong><\/p>\n<ul>\n<li>Test dimensionality has implications for the scoring:<\/li>\n<\/ul>\n<p>o Scoring o Evaluation and o Use of the test scores<\/p>\n<ul>\n<li>Multidimensional tests with correlated dimensions can produce a variety of scores<\/li>\n<\/ul>\n<p>o Subtest score \u2013 based on the items of a single dimension o Area score- based on the items of a single dimension o Total score \u2013 used in higher order composite scores<\/p>\n<p><strong>The psychological meaning of dimensions:<\/strong><\/p>\n<ul>\n<li>After the number of dimensions have been determined<\/li>\n<li>And the associations between the dimensions have been determined<\/li>\n<li>It is now time to understand the psychological meaning of each test dimension<\/li>\n<li>This is accomplished by evaluating which items load onto each respective dimension<\/li>\n<\/ul>\n<p><strong>Inter item correlations (hypothetical):<\/strong><\/p>\n<ul>\n<li>Furthermore, it appears that the two dimensions are not correlated with each other<\/li>\n<li>This is an eye-ball approach to conducting a factor analysis<\/li>\n<li>In practice, it is not especially useful because <strong>o <\/strong>There are usually a lot more than six variables included in a factor analysis <strong>o <\/strong>The pattern of correlation is not usually as clear cut as those in the above table<\/li>\n<\/ul>\n<p><strong>Conducting a principle component analysis (PCA):<\/strong><\/p>\n<ul>\n<li>Note a PCA is almost equivalent to a factor analysis<\/li>\n<li>Conduct a PCA twice:<\/li>\n<\/ul>\n<p>o rnce to determine the number of components (factors) to extract o Then again based on the number of components that you want extracted<\/p>\n<ul>\n<li>Find the break in the scree plot, this separation is obvious to how many dimensions are in the data o Scree plot consists of the eigenvalues ordered from smallest to largest in a scatter plot<\/li>\n<\/ul>\n<p>o Eigenvalues are essentially numerical representations of components with respect to their size.<\/p>\n<ul>\n<li>Now that I know how many components to extract from analysis, rerun with the specification of two components.<\/li>\n<\/ul>\n<p><strong>Communalities:<\/strong><\/p>\n<ul>\n<li>Represent the percentage of variance associated with a particular variable that was included in the analysis<\/li>\n<li>Generally, want to see communalities that or at least .04 or .09 (depending on the type of data being analysed:\n<ul>\n<li>.04 or greater for items<\/li>\n<li>.09 or greater for subscales<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Component landings:<\/strong><\/p>\n<ul>\n<li>Are useful when greater than either .20 or .30\n<ul>\n<li>.20 for items<\/li>\n<li>.30 for subscales<\/li>\n<li>Hence the minimum expectation of a communality of either .04 or .09 o Communality = sum of the squared component landings<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Simple structure:<\/strong><\/p>\n<ul>\n<li>The degree to which an item (or scale or any variable included in the analysis) is associated with only one substantial loading on a single dimension (i.e. component) and negligible loadings on the remaining dimensions<\/li>\n<li>rne way to achieve simple structure is to rotate the solution, should always be done<\/li>\n<li>You can only rotate a solution if you extract two or more components<\/li>\n<\/ul>\n<p><strong>Component correlations:<\/strong><\/p>\n<ul>\n<li>The correlation between the two components is equal to zero<\/li>\n<li>They are two totally separate dimensions with no overlap<\/li>\n<li>You cannot predict how high someone might score on openness to experience if you know how high they were on extraversion<\/li>\n<\/ul>\n<p><strong>Sample size requirements:<\/strong><\/p>\n<ul>\n<li>There are no simple guidelines to follow, because the size of the sample required will be dependent upon two main factors o The amount of communality associated with the variables (higher communality means less sample size required)<\/li>\n<\/ul>\n<p>o The number of variables per factor (higher number of variables per factor means less sample size required)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is relevant to determining whether the scores of a measure correspond to the number and nature of dimensions of theorised dimensions that underlie the construct of interest Researchers use&hellip; <a class=\"continue\" href=\"https:\/\/www.amyork.ca\/academic\/zz\/psychological-measurement\/factorial-validity\/\">Continue Reading<span> Factorial validity<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[107],"tags":[],"_links":{"self":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4284"}],"collection":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/comments?post=4284"}],"version-history":[{"count":0,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/posts\/4284\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/media?parent=4284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/categories?post=4284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.amyork.ca\/academic\/zz\/wp-json\/wp\/v2\/tags?post=4284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}