Aligning constructs

Description
The direction of the constructs in a grid is arbitrary and a reflection of a scale does not affect the information contained in the grid. Nonetheless, the direction of a scale has an effect on inter-element correlations (Mackay, 1992) and on the spatial representation and clustering of the grid (Bell, 2010). Hence, it is desirable to follow a protocol to align constructs that will render unique results. A common approach is to align constructs by pole preference, i.e. aligning all positive and negative poles. This can e. g. be achieved using the function swapPoles. If an ideal element is present the function alignByIdeal will align the constructs accordingly. Note that this approach does not always yield definite results as sometimes ratings do not show a clear preference for one pole (Winter, Bell & Watson, 2010). If a preference cannot be determined definitely, the construct direction remains unchanged (a warning is issued in that case).

Bell (2010) proposed another solution for the problem of construct alignment. As a unique protocol he suggests to align constructs in a way so they all have positive loadings on the first component of a grid PCA.

Align by preference
To align a construct by preference, an ideal element has to be defined. For the following example it is element 13 (ideal self). > alignByIdeal(feixas2004, 13)

META DATA: Number of constructs: 20 Number of elements: 13

SCALE INFO: The grid is rated on a scale from 1 (left pole) to 7 (right pole) using steps of

RATINGS: 7 - Friend 2 Friend 1 - 6 | 8 - Non-grata Boyfriend - 5 | | | 9 - Friend 3 Brother - 4 | | | | | 10 - Cousin Father - 3 | | | | | | | 11 - Godmother Mother - 2 | | | | | | | | | 12 - Friend 4 Self now - 1 | | | | | | | | | | | 13 - Ideal Self | | | | | | | | | | | | |                      Pessimistic (1)   1 1 5 2 7 3 6 2 6 4 3 2 7   (1) Optimistic Self-demanding (2)  1 6 6 2 2 5 6 3 5 6 4 5 4   (2) Takes it easy Fearful (3)  2 2 6 2 4 5 6 5 2 3 4 5 5   (3) Enterprising Lives to work (4)  5 1 2 2 6 6 6 1 6 7 6 6 7   (4) Works to live his/her wishes (5)  6 2 1 1 4 3 6 1 7 3 4 2 7   (5) Tolerant with Touchy (6)  6 1 7 2 4 5 4 2 5 5 3 2 5   (6) Teasing reciate others (7)  6 2 2 2 7 3 4 1 4 6 6 3 7   (7) Appreciates o    Aggressive (8)   6 4 2 2 7 4 6 2 6 6 6 3 7   (8) Calm Selfish (9)  6 6 2 1 6 5 3 1 5 5 6 6 6   (9) Concerned abo Avaricious (10)  6 1 1 1 7 5 5 1 6 3 3 6 7   (10) Generous , superficial (11)  7 3 1 1 7 4 3 1 7 4 5 4 7   (11) Sensitive Cheeky (12)  6 6 5 4 6 6 6 1 6 5 6 5 7   (12) Respectful Hypocritical (13)  5 4 4 2 6 5 5 1 6 6 5 4 7   (13) Sincere Blackmailer (14)  3 2 2 1 5 6 6 1 6 6 6 3 7   (14) Non blackmai onger than is (15)  6 3 1 2 5 2 4 2 7 6 6 5 6   (15) Natural er the friend (16)  6 3 3 3 6 2 1 2 4 4 6 4 7   (16) Looks after on Accessible (17)  5 2 2 1 4 2 4 1 6 3 5 2 7   (17) Accessible Introverted (18)  1 2 6 2 4 5 7 5 2 6 6 5 5   (18) Extroverted ressed easily (19)  1 2 6 3 6 3 7 6 1 3 3 3 6   (19) Does not get the negative (20)  2 2 4 2 7 3 6 1 2 5 5 3 7   (20) Tries to fin

Warnmeldung: In alignByIdeal(feixas2004, 13) : The following constructs do not show a preference for either poleand have thus not been aligned: 2

Note that when midpoint ratings are present no prefrerred pole can be identified, as it is the case for one construct in the example above.

As a default the preferred poles are assigned to the right side. You can use the argument high=FALSE to indicate that high ratings will correspond to the negative pole. Hence, the preferred pole will be oin the left side of the grid. alignByIdeal(feixas2004, 13, high=F)

To save the assigned grid into a new object: x <- alignByIdeal(feixas2004, 13)

Align by loadings
The alignment operation using OpenRepgrid is performed by the function alignByLoadings. As a default the function will return a grid with aligned constructs. To get more information about the function type: ?alignByLoadings to the console to open the help menu for the function.

> alignByLoadings(bell2010)

META DATA: Number of constructs: 9 Number of elements: 10

SCALE INFO: The grid is rated on a scale from 1 (left pole) to 7 (right pole) using steps of

RATINGS: A teacher you respected - 5 6 - Mother (or the person who on of the opposite sex t - 4 | | 7 - A person of the opposit ppiest person you know - 3 | | | | 8 - The most confident pe iend of the same sex - 2 | | | | | | 9 - A person you work w             self - 1 | | | | | | | | 10 - A teacher you di                     | | | | | | | | | |                           relaxed (1)   4 4 6 5 3 6 5 2 2 6   (1) worried & ten (academically) (2)   2 1 2 3 1 4 2 1 4 1   (2) not so smart islikes sports (3)   6 3 7 6 4 4 2 3 6 3   (3) loves sports   loves people (4)   2 1 3 2 2 3 2 1 1 4   (4) not interacti ot transparent (5)   6 4 5 7 3 7 6 5 6 3   (5) transparent     insensitive (6)   4 6 5 4 4 6 5 3 4 2   (6) sensitive          fearless (7)   3 4 4 2 3 5 3 2 3 3   (7) fearful&timid         rough (8)   5 6 6 4 5 7 7 3 5 6   (8) gentle       loves to argue (9)   3 3 2 1 4 4 2 1 3 3   (9) accept as it

To save the aligned grid in an object: > x <- alignByLoadings(bell2010) > x

To print the intermediate results of the calculation to the use output=1. The command renders the following output in the R console. This is an exact reproduction of the output produced by Bell's gridstat program as found in Bell (2010).

> alignByLoadings(bell2010, out=1)

Alignment of constructs by loadings

Construct correlations - before alignment

1   2    3    4    5    6    7    8    9 (1) relaxed - worried &        -0.1  0.0 -0.8  0.1  0.2 -0.5  0.7 -0.1 (2) not so sma - smart (aca        -0.5  0.0 -0.8 -0.3  0.3 -0.2  0.1 (3) dislikes s - loves spor               0.0  0.4  0.0  0.0 -0.2  0.1 (4) not intera - loves peop                    0.2  0.2  0.3 -0.5  0.2 (5) not transp - transparen                         0.4  0.0  0.0  0.3 (6) insensitiv - sensitive                              -0.7  0.5 -0.3 (7) fearful&ti - fearless                                    -0.8  0.7 (8) rough - gentle                                                -0.5 (9) accept as  - loves to a

Construct factor loadiongs on PC1 - before alignment

PC1 relaxed - worried &     0.7 not so sma - smart (aca -0.4 dislikes s - loves spor 0.0 not intera - loves peop -0.5 not transp - transparen  0.2 insensitiv - sensitive   0.6 fearful&ti - fearless   -0.9 rough - gentle           0.9 accept as  - loves to a -0.6

The following constructs are reversed:

index not so sma - smart (aca    2 not intera - loves peop     4 fearful&ti - fearless       7 accept as  - loves to a     9

Construct correlations - after alignment

1   2    3    4    5    6    7    8    9 (1) relaxed - worried &         0.1  0.0  0.8  0.1  0.2  0.5  0.7  0.1 (2) smart (aca - not so sma         0.5  0.0  0.8  0.3  0.3  0.2  0.1 (3) dislikes s - loves spor               0.0  0.4  0.0  0.0 -0.2 -0.1 (4) loves peop - not intera                   -0.2 -0.2  0.3  0.5  0.2 (5) not transp - transparen                         0.4  0.0  0.0 -0.3 (6) insensitiv - sensitive                               0.7  0.5  0.3 (7) fearless - fearful&ti                                     0.8  0.7 (8) rough - gentle                                                 0.5 (9) loves to a - accept as

Construct factor loadings on PC1 - after alignment

PC1 relaxed - worried &    0.7 smart (aca - not so sma 0.4 dislikes s - loves spor 0.0 loves peop - not intera 0.5 not transp - transparen 0.2 insensitiv - sensitive 0.6 fearless - fearful&ti   0.9 rough - gentle          0.9 loves to a - accept as  0.6

output=2 will return the intermediate results as single data frame in a list. This may be useful for further processing of the results. > res <- alignByLoadings(bell2010, out=2) > res

Literature

 * Bell, R. C. (2010). A note on aligning constructs. Personal Construct Theory & Practice, 7, 42-48.
 * Mackay, N. (1992). Identification, Reflection, and Correlation: Problems in the bases of repertory grid measures. International Journal of Personal Construct Psychology, 5(1), 57-75.
 * Winter, D. A., Bell, R. C., & Watson, S. (2010). Midpoint ratings on personal constructs: Constriction or the middle way? Journal of Constructivist Psychology, 23(4), 337-356.