Discourses on Addiction among Gamblers and Drug Users in Treatment. An Analysis of the Interviews through Constrained Correspondence Analysis

Abstract

In this paper, a study on 40 semi-structured interviews with users of the Italian health services and self-help groups is presented to gain a deeper insight on how members describe, understand, and face their problems with substance or behavioral addiction. A simple correspondence analysis (CA) was applied to the transcripts of the interviews to detect the main dimensions of sense which organize the users’ discourse about their problem and their request for help. In addition, constraint correspondence analysis (CCA) was applied to evaluate whether these dimensions are affected by the kind of help context the users belong to, type of addiction, age, and gender. No substantial differences emerged from CA and CCA. Results show that the users’ discourses focus on two different kinds of experience: the substance or gambling problem and the experience of being helped. Furthermore, dis/similarity in the user discourses concerns the way of symbolizing the problem motivating the request for help, identified with the addiction or with the breakup of one’s family and social relationships. Through the interviews, a view of addiction as a disorder affects the way users define their problem and define the goal of the treatment.

Appendix

We first describe CA without constraints to introduce the notation used for explaining CCA. Consider an I by J contingency table P with proportions p describing the distribution of two categorical variables, X and Y, with I and J categories. Let D _r and D _c be diagonal matrices containing the row and column sums of P. CA is the generalized singular value decomposition (GSVD) of

$$ \mathbf{A}={\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}}\ \left(\mathbf{P}\hbox{--} \mathbf{E}\right)\ {\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}}=\mathbf{R}\ {\boldsymbol{D}}_{\uplambda}{\boldsymbol{C}}^{\prime } $$

(1)

with E = D _r 1 1^′D _c (where 1 is a unit vector) and D_λis a diagonal matrix with min (I − 1, J − 1) singular values λ in descending order.

The standard row and column coordinates, R and C, satisfy the restrictions R^′D _r  R = I = C^′D _c  C and 1^′D _r R = 0 = 1^′D _c  C.

The coordinates are computed by an ordinary SVD of the matrix Z:

$$ \mathbf{Z}={\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}/\mathbf{2}}\ \left(\mathbf{P}\hbox{--} \mathbf{E}\right)\ {\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}/\mathbf{2}}=\mathbf{U}\ {\boldsymbol{D}}_{\uplambda}{\boldsymbol{V}}^{\prime } $$

(2)

with U^′ U = I = V^′ V , and

$$ \mathbf{R}={\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}/\mathbf{2}}\ \boldsymbol{U} $$

(3)

and

$$ \mathrm{C}={\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}/\mathbf{2}}\ \boldsymbol{V} $$

(4)

According to the null-space method, linear row and column constraints are defined by

$$ {\boldsymbol{G}}^{\prime }{\boldsymbol{R}}^{\ast }=\mathbf{0} $$

(5)

and

$$ {\boldsymbol{H}}^{\prime }{\boldsymbol{C}}^{\ast }=\mathbf{0} $$

(6)

where G is a known I × K matrix of rank K. Similarly, H is a known J × L matrix of rank L. The effects defined by the matrices G and H are partialed out from the standard row and column scores denoted by R^∗andC^∗, respectively, by computing the complementary projection operators Q _r and Q _c :

$$ {\boldsymbol{Q}}_{\boldsymbol{r}}=\mathbf{I}\hbox{--} \mathbf{G}\ {\left({\boldsymbol{G}}^{\prime }{\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}}\boldsymbol{G}\right)}^{-\mathbf{1}}{\boldsymbol{G}}^{\prime }{\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}} $$

(7)

and

$$ {\boldsymbol{Q}}_{\boldsymbol{c}}=\mathbf{I}\hbox{--} \mathbf{H}\ {\left({\boldsymbol{H}}^{\prime }{\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}}\boldsymbol{H}\right)}^{-\mathbf{1}}{\boldsymbol{H}}^{\prime }{\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}} $$

(8)

The constrained standard scores are then obtained by the SVD of

$$ {\boldsymbol{Z}}^{\ast }={\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}/\mathbf{2}}{\boldsymbol{Q}}_{\boldsymbol{r}}\ \left(\boldsymbol{P}\hbox{--} \boldsymbol{E}\right)\ {\boldsymbol{Q}}_{\boldsymbol{c}}^{\prime }{\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}/\mathbf{2}}={\boldsymbol{U}}^{\ast }{\boldsymbol{D}}_{\lambda}^{\ast }{\boldsymbol{V}}^{\ast \prime } $$

(9)

with U^∗′U^∗ = I = V^∗′V^∗, yielding

$$ {\boldsymbol{R}}^{\ast }={\boldsymbol{D}}_{\boldsymbol{r}}^{-\mathbf{1}/\mathbf{2}}{\boldsymbol{U}}^{\ast } $$

(10)

and

$$ {\boldsymbol{C}}^{\ast }={\boldsymbol{D}}_{\boldsymbol{c}}^{-\mathbf{1}/\mathbf{2}}{\boldsymbol{V}}^{\ast } $$

(11)

and, consequently,

$$ {\boldsymbol{R}}^{\ast \prime }{\boldsymbol{D}}_{\boldsymbol{r}}{\boldsymbol{R}}^{\ast }=\mathbf{I}={\boldsymbol{C}}^{\ast \prime }{\boldsymbol{D}}_{\boldsymbol{c}}{\boldsymbol{C}}^{\ast } $$

(12)

and

$$ {1}^{\prime }{\boldsymbol{D}}_{\boldsymbol{r}}{\boldsymbol{R}}^{\ast }=\mathbf{0}={1}^{\prime }{\boldsymbol{D}}_{\boldsymbol{c}}{\boldsymbol{C}}^{\ast }. $$

(13)

If constraints are imposed only on the row scores H = D _c 1 and, similarly, if constraints are imposed only on the column scores G = D _r 1. Thus, the matrices, Z^∗and Z are identical when G = D _r 1 and H = D _c 1 (Greenacre 1984).