{"id":5269,"date":"2026-03-19T20:16:15","date_gmt":"2026-03-19T19:16:15","guid":{"rendered":"https:\/\/www.psyctc.org\/psyctc\/?post_type=docs&p=5269"},"modified":"2026-03-19T20:16:15","modified_gmt":"2026-03-19T19:16:15","password":"","slug":"loading","status":"publish","type":"docs","link":"https:\/\/www.psyctc.org\/psyctc\/glossary2\/loading\/","title":{"rendered":"Loading"},"content":{"rendered":"\n

You will see this term in factor, principal component and linear regression analyses. There is a consistent meaning across those various, rather different, statistical analyses though that may not be immediately obvious. <\/p>\n\n\n\n

The basic idea in all these analyses is that a loading tells you how much, statistically, across the dataset, differences in the values of one variable appear to contribute to differences in another variable. It’s about statistical associations which may or may not be causal, it’s not about a relationship for any one participant whose data was in the data, equally, it doesn’t predict the relationship there will be between scores on the variables for any other person not in the dataset. However, given a lot of assumptions, it gives you a least worst prediction about how the same variables might be associated in future datasets.<\/p>\n\n\n\n

As it’s used a lot, and as it can seem to mean something rather different from what it actually describes, I’m expanding on the meaning of the term here.<\/p>\n\n\n\n

Details<\/h4>\n\n\n\n

The basic idea is that a loading represents how much variance a particular variable appears to contribute to the variance of another one. Let’s start with a (simulated) example from linear regression. Suppose were looking at the relationship between baseline weight (in kg) to height (in m) across a dataset of 450 clients with eating disorder problems presenting for help. The data might look like this.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

That looks like a fair approximation to a linear relationship. (It should: it’s simulated Gaussian data but based on emerging correlation, means and SDs from the ITAMITED study: Grau Touri\u00f1o, A., Feixas, G., Medina, J. C., Paz, C., & Evans, C. (2021). Effectiveness of integrated treatment for eating disorders in Spain: Protocol for a multicentre, naturalistic, observational study. BMJ Open<\/em>, 11<\/em>(3), e043152. https:\/\/doi.org\/10.1136\/bmjopen-2020-043152<\/a>.) If we ask R for the linear regression it tells me that the relationship is:<\/p>\n\n\n\n

Weight<\/mtext>=<\/mo>68.57<\/mn>\u2217<\/mo>Height<\/mtext>\u2212<\/mo>59.33<\/mn><\/mrow>\\text{Weight}=68.57*\\text{Height}-59.33<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

So these data suggest that there is a systematic relationship between height and weight with weight in kg being 68.57 times height in metres minus 59.33. Here we can regard 68.57 as a loading of height on weight meaningful in the two units of measurement. The key thing to realise is that it doesn’t say that if you are 2m tall your weight will be 77.81kg, nor that if you grow another cm you will increase in weight by .6857kg. Roughly speaking, loadings are regression weights and about relationships across datasets not about individual’s data.<\/p>\n\n\n\n

Sometimes it may be reasonable to believe that there is an element of causality in the relationship, to a limited extent that seems not unreasonable here, however, causality is not a necessary aspect of a loading, only directionality: this particular relationship looks at a relationship from <\/em>height to <\/em>weight, not a correlation between the two.<\/p>\n\n\n\n

So we can look at the reversed regression.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
Weight<\/mtext>=<\/mo>75.58<\/mn>\u2217<\/mo>Height<\/mtext>\u2212<\/mo>69.51<\/mn><\/mrow>\\text{Weight}=75.58*\\text{Height}- 69.51<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

So we have two possible ways of looking for a regression, directional relationship, here and we have the dimensionless, directionless correlation (here the Pearson correlation between height and weight is .36).<\/p>\n\n\n\n

You don’t usually see simple linear regression reports using the term “loading” but you could. You see the term more often in factor and prinicipal component analyses and “structural equation modelling”. In all these analyses the term has the same meaning as in the example above. If we see that the loading of the first item of the Hospital Anxiety and Depression Scales on the first principal component is .67 (see glossary entry for PCA<\/a>) what it means is that the regression of scores of that item on this first component is .67. As the item data have (usually) been standardised to have variance 1 and as I set the variance of the principal components to 1 this means that this is a pretty strong relationship:<\/p>\n\n\n\n

Item 1 score<\/mtext>=<\/mo>.67<\/mn>\u2217<\/mo>P<\/mi>C<\/mi>1<\/mn>+<\/mo>e<\/mi>r<\/mi>r<\/mi>o<\/mi>r<\/mi><\/mrow>\\text{Item 1 score} = .67*PC1 + error<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

The same principal will apply to the term in the various other analyses in which you’ll see it.<\/p>\n\n\n\n

Cautionary notes to remember about any loading<\/h5>\n\n\n\n

Directionality<\/strong>: Always remember that it’s direction and from<\/em> the putatative common component or factor (depending on the type of analysis) to<\/em> the item score. That’s following from the assumption behind the design of the measure: that the scores on the items are reflections of shared variance that can’t be directly measured. <\/p>\n\n\n\n

Causality<\/strong>: It’s equally important to remember is that loadings may or may not reflect a causal effect. Your assumptions and the design of the data collection are the only things that can translate loadings into indications of causal.<\/p>\n\n\n\n

The “ecological fallacy”<\/strong>: even if the relationship is causal the effect is statistical, it’s a generality across the data points, in our field, usually participants. It’s not telling us about a force or effect that will necessarily behave in this way for any individual. (That’s where that “error<\/em>” comes in in the equation above.)<\/p>\n\n\n\n

Try also<\/h4>\n\n\n\n