Analysis of studies referenced by P.R.Amato, Sacred Cows, chapter 4.

1
Davies L, Avison W.R., McAlpine D.D. Significant life experiences and depression among single and married mothers. Journal of Marriage and the Family 59 (May 1997): 294—308
Does this study show that divorce causes people to be more unhappy than they would have been if they had remained married?
No. To begin with, this paper is not even about divorce. It's about depression among single mothers. Some of the subjects in the study had been divorced, but authors made no attempt to show the effects of divorce on depression. Furthermore, the single mothers had far lower income levels and a far higher incidence of childhood emotional trauma than married mothers. That means that the authors were comparing apples to oranges. If an apple gets divorced and an orange stays married, can we ascribe the color of the fruit to its marital status? We think not.
What did the authors do?
The authors recruited 518 single mothers (some never married, some separated, some divorced) and 502 married mothers from 13 geographic areas within the city of London, Canada. Subjects were stratified by the age and gender of the oldest child. The women were then interviewed in their homes and asked questions about symptoms of depression, history of depression, history of childhood adversity including things like assault, abortion, death/divorce of parents, parental substance abuse, poor maternal or paternal attachment.
What did the authors find?
The authors recruited 518 single mothers (some never married, some separated, some divorced) and 502 married mothers from 13 geographic areas within the city of London, Canada. Subjects were stratified by the age and gender of the oldest child. The women were then interviewed in their homes and asked questions about symptoms of depression, history of depression, history of childhood adversity including things like assault, abortion, death/divorce of parents, parental substance abuse, poor maternal or paternal attachment. The authors reported that single mothers had less education, fewer children and significantly less income than married mothers (by a factor of nearly 3). Single mothers were more likely to report recent and well as recurrent depression, and the onset of depression was more likely to be at an early age ("21 years of age) compared with married mothers with depression. They also reported significantly lower attachment to their parents, more parental depression and more parental substance abuse. A quarter of them had been assaulted in childhood, compared with 13% of married respondents, and 10% had terminated pregnancies in childhood, compared with 2.4% of married mothers. The authors did not detect differences between the never married and the separated/divorced single mothers except in age of onset of depression, history of parental depression and history of parents being separated.
What can we conclude from this study?
In the population chosen for study, childhood traumas, low income and early onset depression correlate with single motherhood. This could mean that people who have difficult childhoods and are predisposed to depression are more likely to have children out of wedlock or to divorce. We can't infer a causal relationship, however. These factors could cluster for some non-causal reason.

The design of the study does not allow the researchers to ask the question "Does choosing to be a single parent cause people to be more depressed?" Presumably most of the single mothers would have chosen to be happily married if that opportunity presented itself. They likely did not say to themselves "I could stay married to/marry my true love, or I could raise my children by myself. I think I'll raise the kids alone!” Presumably they had to choose between two difficult options, and it is not knowable whether they would have been happier had they chosen difficult option #1 over difficult option #2. Some of the married women in the study may have made the difficult decision to stay in an unhappy marriage, but presumably many of them have never considered getting divorced. These women may be advantaged beyond their relative wealth and psychological well being, in that a number of them may have happy marriages.

Finally, this study is focused entirely on mothers. The findings cannot be extrapolated to men or to childless women.
2
Kitson, 1992 Portrait of Divorce: Adjustment to marital breakdown
This is a book about divorce written by a sociologist; it is not a peer-reviewed study.
3
Robins, L. N., & Regier, D. A. (1991). Psychiatric disorders in America: the epidemiologic catchment area study.
This is a book documenting various psychiatric disorders afflicting Americans. It is not a peer-reviewed study and not, so far as we can tell, about marriage and divorce.
4
Shapiro AD. Explaining psychological distress in a sample of remarried and divorced persons. Journal of Family Issues Vol 17 (2) 1996 186—203
Does this study show that divorce causes people to be more unhappy than they would have been if they had remained married?
No. The authors were not even asking that question. The authors were wondering whether remarriage causes people to feel less distressed than they might have felt before remarriage, and if so, whether the difference is caused by having more money.
What did the authors do?
Interviews were conducted with 319 remarried individuals, 276 currently divorced individuals and 1486 currently married never-divorced individuals. They asked respondents questions such as "How often in the last week did you experience depression/loneliness/enjoyment" etc. They also collected information about income and about how economically distressed these same people felt (e.g. whether the respondents found it hard to pay their bills each month). It is impossible to say how they analyzed the data, because the authors did not provide sufficient detail. They report regression coefficients for "effects of divorce and remarriage on economic distress" and for "estimated effects of divorce, remarriage and economic distress on depression," but they do not explain how they set up the models, and they do not share the raw data.
What did the authors find?
Since we can't verify that the authors handled their data appropriately, we can only take it on faith that they found what they claim to have found. The authors conclude that "depression levels among the remarried are significantly lower than those of the currently divorced, and that "the remarried have significantly lower rates of both objective and subjective economic distress than do the currently divorced." They also concluded that "After controlling for income differences, there are no significant differences in psychological distress between the remarried and currently divorced."
What can we conclude from this study?
Assuming that the data were analyzed correctly, we can conclude that for this small sample set of individuals, people who did not remarry after divorce were relatively poorer and relatively less happy than people who did remarry after divorce. Poverty and unhappiness were correlated, and once the authors tried to "control" for poverty, the difference in happiness went away. Because this is a cross-sectional study, we can’t conclude anything about cause and effect. The people who remarried might have been wealthier and happier to begin with, or their remarriage may have caused wealth and happiness. People who remained divorced might not have remarried because they were poor and unhappy, or their lack of a spouse may have caused their poverty and unhappiness. Their poverty might have caused their unhappiness, but it's also possible that their unhappiness caused their poverty, or that both were caused by some third unmeasured variable, like physical disability or lack of social support. In the end, all we can really conclude is that individuals in the study group who did not remarry after divorce tended to be poorer and less happy than people who did remarry.